Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x^3-64*x=0
-
Equation 3x^2=2x+x^3
-
Equation 4x^3-4x=0
-
Equation 4*x-8=x+1
- Express {x} in terms of y where:
- -2*x-5*y=16
- -8*x+13*y=7
- -5*x-14*y=6
- 6*x+10*y=-19
-
Identical expressions
- x^ two +x*y- two *y^ two -x+y= three
- x squared plus x multiply by y minus 2 multiply by y squared minus x plus y equally 3
- x to the power of two plus x multiply by y minus two multiply by y to the power of two minus x plus y equally three
- x2+x*y-2*y2-x+y=3
- x²+x*y-2*y²-x+y=3
- x to the power of 2+x*y-2*y to the power of 2-x+y=3
- x^2+xy-2y^2-x+y=3
- x2+xy-2y2-x+y=3
-
Similar expressions
- x^2-x*y-2*y^2-x+y=3
- x^2+x*y+2*y^2-x+y=3
- x^2+x*y-2*y^2+x+y=3
- x^2+x*y-2*y^2-x-y=3
x^2+x*y-2*y^2-x+y=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 2 x + x*y - 2*y - x + y = 3
$$y + \left(- x + \left(- 2 y^{2} + \left(x^{2} + x y\right)\right)\right) = 3$$
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$y + \left(- x + \left(- 2 y^{2} + \left(x^{2} + x y\right)\right)\right) = 3$$
to
$$\left(y + \left(- x + \left(- 2 y^{2} + \left(x^{2} + x y\right)\right)\right)\right) - 3 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = y - 1$$
$$c = - 2 y^{2} + y - 3$$
, then
The equation has two roots.
or
$$x_{1} = - \frac{y}{2} + \frac{\sqrt{8 y^{2} - 4 y + \left(y - 1\right)^{2} + 12}}{2} + \frac{1}{2}$$
$$x_{2} = - \frac{y}{2} - \frac{\sqrt{8 y^{2} - 4 y + \left(y - 1\right)^{2} + 12}}{2} + \frac{1}{2}$$
left part with negative sign.
The equation is transformed from
$$y + \left(- x + \left(- 2 y^{2} + \left(x^{2} + x y\right)\right)\right) = 3$$
to
$$\left(y + \left(- x + \left(- 2 y^{2} + \left(x^{2} + x y\right)\right)\right)\right) - 3 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = y - 1$$
$$c = - 2 y^{2} + y - 3$$
, then
D = b^2 - 4 * a * c =
(-1 + y)^2 - 4 * (1) * (-3 + y - 2*y^2) = 12 + (-1 + y)^2 - 4*y + 8*y^2
The equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{y}{2} + \frac{\sqrt{8 y^{2} - 4 y + \left(y - 1\right)^{2} + 12}}{2} + \frac{1}{2}$$
$$x_{2} = - \frac{y}{2} - \frac{\sqrt{8 y^{2} - 4 y + \left(y - 1\right)^{2} + 12}}{2} + \frac{1}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = y - 1$$
$$q = \frac{c}{a}$$
$$q = - 2 y^{2} + y - 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1 - y$$
$$x_{1} x_{2} = - 2 y^{2} + y - 3$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = y - 1$$
$$q = \frac{c}{a}$$
$$q = - 2 y^{2} + y - 3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1 - y$$
$$x_{1} x_{2} = - 2 y^{2} + y - 3$$
The graph
Rapid solution
[src]
/ ______________________________________________________________________ \ ______________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|| 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|
| \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *sin|--------------------------------------------------------------------|| \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *cos|--------------------------------------------------------------------|
1 re(y) | im(y) \ 2 /| \ 2 /
x1 = - - ----- + I*|- ----- - ----------------------------------------------------------------------------------------------------------------------------------------------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------
2 2 \ 2 2 / 2
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) - \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{1}{2}$$
/ ______________________________________________________________________ \ ______________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|| 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|
| \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *sin|--------------------------------------------------------------------|| \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *cos|--------------------------------------------------------------------|
1 re(y) | im(y) \ 2 /| \ 2 /
x2 = - - ----- + I*|- ----- + ----------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------
2 2 \ 2 2 / 2
$$x_{2} = i \left(\frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) + \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{1}{2}$$
x2 = i*(((18*re(y)*im(y) - 6*im(y))^2 + (9*re(y)^2 - 6*re(y) - 9*im(y)^2 + 13)^2)^(1/4)*sin(atan2(18*re(y)*im(y) - 6*im(y, 9*re(y)^2 - 6*re(y) - 9*im(y)^2 + 13)/2)/2 - im(y)/2) + ((18*re(y)*im(y) - 6*im(y))^2 + (9*re(y)^2 - 6*re(y) - 9*im(y)^2 + 13)^2)^(1/4)*cos(atan2(18*re(y)*im(y) - 6*im(y), 9*re(y)^2 - 6*re(y) - 9*im(y)^2 + 13)/2)/2 - re(y)/2 + 1/2)
Sum and product of roots
[src]
sum
/ ______________________________________________________________________ \ ______________________________________________________________________ / ______________________________________________________________________ \ ______________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|| 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/| | 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|| 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|
| \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *sin|--------------------------------------------------------------------|| \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *cos|--------------------------------------------------------------------| | \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *sin|--------------------------------------------------------------------|| \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *cos|--------------------------------------------------------------------|
1 re(y) | im(y) \ 2 /| \ 2 / 1 re(y) | im(y) \ 2 /| \ 2 /
- - ----- + I*|- ----- - ----------------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------- + - - ----- + I*|- ----- + ----------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------
2 2 \ 2 2 / 2 2 2 \ 2 2 / 2
$$\left(i \left(- \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) - \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{1}{2}\right) + \left(i \left(\frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) + \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{1}{2}\right)$$
=
/ ______________________________________________________________________ \ / ______________________________________________________________________ \
| / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
| 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|| | 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/||
| \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *sin|--------------------------------------------------------------------|| | \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *sin|--------------------------------------------------------------------||
| im(y) \ 2 /| | im(y) \ 2 /|
1 - re(y) + I*|- ----- + ----------------------------------------------------------------------------------------------------------------------------------------------------| + I*|- ----- - ----------------------------------------------------------------------------------------------------------------------------------------------------|
\ 2 2 / \ 2 2 /
$$i \left(- \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) + i \left(\frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) - \operatorname{re}{\left(y\right)} + 1$$
product
/ / ______________________________________________________________________ \ ______________________________________________________________________ \ / / ______________________________________________________________________ \ ______________________________________________________________________ \ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|| 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|| | | 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|| 4 / 2 / 2 2 \ |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|| | | \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *sin|--------------------------------------------------------------------|| \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *cos|--------------------------------------------------------------------|| | | \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *sin|--------------------------------------------------------------------|| \/ (-6*im(y) + 18*im(y)*re(y)) + \13 - 9*im (y) - 6*re(y) + 9*re (y)/ *cos|--------------------------------------------------------------------|| |1 re(y) | im(y) \ 2 /| \ 2 /| |1 re(y) | im(y) \ 2 /| \ 2 /| |- - ----- + I*|- ----- - ----------------------------------------------------------------------------------------------------------------------------------------------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------|*|- - ----- + I*|- ----- + ----------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------| \2 2 \ 2 2 / 2 / \2 2 \ 2 2 / 2 /
$$\left(i \left(- \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) - \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{1}{2}\right) \left(i \left(\frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) + \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{1}{2}\right)$$
=
2 2 -3 - 2*re (y) + 2*im (y) + I*im(y) - 4*I*im(y)*re(y) + re(y)
$$- 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{re}{\left(y\right)} + 2 \left(\operatorname{im}{\left(y\right)}\right)^{2} + i \operatorname{im}{\left(y\right)} - 3$$
-3 - 2*re(y)^2 + 2*im(y)^2 + i*im(y) - 4*i*im(y)*re(y) + re(y)