Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -x^2-4*x-3=0
-
Equation cos(x)=-3
-
Equation sin(-x)=0
-
Equation (x+3)^3=81*(x+3)
- Express {x} in terms of y where:
- -15*x+9*y=18
- 19*x-1*y=9
- -1*x-19*y=-7
- -19*x-4*y=17
- Derivative of:
-
sqrt(1-2x)
- Graphing y =:
- sqrt(1-2x)
- Integral of d{x}:
- sqrt(1-2x)
-
Identical expressions
- sqrt(one -2x)=a-11absolute(x)
- square root of (1 minus 2x) equally a minus 11absolute(x)
- square root of (one minus 2x) equally a minus 11absolute(x)
- √(1-2x)=a-11absolute(x)
- sqrt1-2x=a-11absolutex
-
Similar expressions
- -x^2/sqrt(1-2*x)+2*x*sqrt(1-2*x)=0
- sqrt(1-2x)=a+11absolute(x)
- (sqrt(1-2*x))*(ln(16*(x*x)-(a*a)))=(sqrt(1-2*x))*(ln(4*x+a))
- sqrt(1+2x)=a-11absolute(x)
sqrt(1-2x)=a-11absolute(x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
_________ \/ 1 - 2*x = a - 11*|x|
$$\sqrt{1 - 2 x} = a - 11 \left|{x}\right|$$
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x \geq 0$$
or
$$0 \leq x \wedge x < \infty$$
we get the equation
$$- a + 11 x + \sqrt{1 - 2 x} = 0$$
after simplifying we get
$$- a + 11 x + \sqrt{1 - 2 x} = 0$$
the solution in this interval:
$$x_{1} = \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121}$$
$$x_{2} = \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121}$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$- a + 11 \left(- x\right) + \sqrt{1 - 2 x} = 0$$
after simplifying we get
$$- a - 11 x + \sqrt{1 - 2 x} = 0$$
the solution in this interval:
$$x_{3} = - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121}$$
$$x_{4} = - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121}$$
The final answer:
$$x_{1} = \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121}$$
$$x_{2} = \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121}$$
$$x_{3} = - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121}$$
$$x_{4} = - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121}$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x \geq 0$$
or
$$0 \leq x \wedge x < \infty$$
we get the equation
$$- a + 11 x + \sqrt{1 - 2 x} = 0$$
after simplifying we get
$$- a + 11 x + \sqrt{1 - 2 x} = 0$$
the solution in this interval:
$$x_{1} = \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121}$$
$$x_{2} = \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121}$$
2.
$$x < 0$$
or
$$-\infty < x \wedge x < 0$$
we get the equation
$$- a + 11 \left(- x\right) + \sqrt{1 - 2 x} = 0$$
after simplifying we get
$$- a - 11 x + \sqrt{1 - 2 x} = 0$$
the solution in this interval:
$$x_{3} = - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121}$$
$$x_{4} = - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121}$$
The final answer:
$$x_{1} = \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121}$$
$$x_{2} = \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121}$$
$$x_{3} = - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121}$$
$$x_{4} = - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121}$$
The graph
Rapid solution
[src]
// ____________ ___ ___________ \ // ____________ ___ ___________ \
|| 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a | || 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a |
||- --- - -- - -------------- for --- + -- + ------------------- > 0| ||- --- - -- - -------------- for --- + -- + ------------------- > 0|
x1 = I*im|< 121 11 121 121 11 121 | + re|< 121 11 121 121 11 121 |
|| | || |
|| nan otherwise | || nan otherwise |
\\ / \\ /
$$x_{1} = \operatorname{re}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// ____________ ___ ___________ \ // ____________ ___ ___________ \
|| 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a | || 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a |
||- --- - -- + -------------- for --- + -- - ------------------- > 0| ||- --- - -- + -------------- for --- + -- - ------------------- > 0|
x2 = I*im|< 121 11 121 121 11 121 | + re|< 121 11 121 121 11 121 |
|| | || |
|| nan otherwise | || nan otherwise |
\\ / \\ /
$$x_{2} = \operatorname{re}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// ____________ ___ ___________ \ // ____________ ___ ___________ \
|| 1 \/ 122 - 22*a a 1 a \/ 2 *\/ 61 - 11*a | || 1 \/ 122 - 22*a a 1 a \/ 2 *\/ 61 - 11*a |
||- --- - -------------- + -- for --- - -- + ------------------- <= 0| ||- --- - -------------- + -- for --- - -- + ------------------- <= 0|
x3 = I*im|< 121 121 11 121 11 121 | + re|< 121 121 11 121 11 121 |
|| | || |
|| nan otherwise | || nan otherwise |
\\ / \\ /
$$x_{3} = \operatorname{re}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
// ____________ ___ ___________ \ // ____________ ___ ___________ \
|| 1 a \/ 122 - 22*a 1 a \/ 2 *\/ 61 - 11*a | || 1 a \/ 122 - 22*a 1 a \/ 2 *\/ 61 - 11*a |
||- --- + -- + -------------- for - --- + -- + ------------------- >= 0| ||- --- + -- + -------------- for - --- + -- + ------------------- >= 0|
x4 = I*im|< 121 11 121 121 11 121 | + re|< 121 11 121 121 11 121 |
|| | || |
|| nan otherwise | || nan otherwise |
\\ / \\ /
$$x_{4} = \operatorname{re}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
x4 = re(Piecewise((a/11 + sqrt(122 - 22*a/121 - 1/121, a/11 + sqrt(2)*sqrt(61 - 11*a)/121 - 1/121 >= 0), (nan, True))) + i*im(Piecewise((a/11 + sqrt(122 - 22*a)/121 - 1/121, a/11 + sqrt(2)*sqrt(61 - 11*a)/121 - 1/121 >= 0), (nan, True))))
Sum and product of roots
[src]
sum
// ____________ ___ ___________ \ // ____________ ___ ___________ \ // ____________ ___ ___________ \ // ____________ ___ ___________ \ // ____________ ___ ___________ \ // ____________ ___ ___________ \ // ____________ ___ ___________ \ // ____________ ___ ___________ \
|| 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a | || 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a | || 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a | || 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a | || 1 \/ 122 - 22*a a 1 a \/ 2 *\/ 61 - 11*a | || 1 \/ 122 - 22*a a 1 a \/ 2 *\/ 61 - 11*a | || 1 a \/ 122 - 22*a 1 a \/ 2 *\/ 61 - 11*a | || 1 a \/ 122 - 22*a 1 a \/ 2 *\/ 61 - 11*a |
||- --- - -- - -------------- for --- + -- + ------------------- > 0| ||- --- - -- - -------------- for --- + -- + ------------------- > 0| ||- --- - -- + -------------- for --- + -- - ------------------- > 0| ||- --- - -- + -------------- for --- + -- - ------------------- > 0| ||- --- - -------------- + -- for --- - -- + ------------------- <= 0| ||- --- - -------------- + -- for --- - -- + ------------------- <= 0| ||- --- + -- + -------------- for - --- + -- + ------------------- >= 0| ||- --- + -- + -------------- for - --- + -- + ------------------- >= 0|
I*im|< 121 11 121 121 11 121 | + re|< 121 11 121 121 11 121 | + I*im|< 121 11 121 121 11 121 | + re|< 121 11 121 121 11 121 | + I*im|< 121 121 11 121 11 121 | + re|< 121 121 11 121 11 121 | + I*im|< 121 11 121 121 11 121 | + re|< 121 11 121 121 11 121 |
|| | || | || | || | || | || | || | || |
|| nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise |
\\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ /
$$\left(\left(\left(\operatorname{re}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) + \left(\operatorname{re}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)\right) + \left(\operatorname{re}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)\right) + \left(\operatorname{re}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
// ____________ ___ ___________ \ // ____________ ___ ___________ \ // ____________ ___ ___________ \ // ____________ ___ ___________ \ // ____________ ___ ___________ \ // ____________ ___ ___________ \ // ____________ ___ ___________ \ // ____________ ___ ___________ \
|| 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a | || 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a | || 1 \/ 122 - 22*a a 1 a \/ 2 *\/ 61 - 11*a | || 1 a \/ 122 - 22*a 1 a \/ 2 *\/ 61 - 11*a | || 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a | || 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a | || 1 \/ 122 - 22*a a 1 a \/ 2 *\/ 61 - 11*a | || 1 a \/ 122 - 22*a 1 a \/ 2 *\/ 61 - 11*a |
||- --- - -- - -------------- for --- + -- + ------------------- > 0| ||- --- - -- + -------------- for --- + -- - ------------------- > 0| ||- --- - -------------- + -- for --- - -- + ------------------- <= 0| ||- --- + -- + -------------- for - --- + -- + ------------------- >= 0| ||- --- - -- - -------------- for --- + -- + ------------------- > 0| ||- --- - -- + -------------- for --- + -- - ------------------- > 0| ||- --- - -------------- + -- for --- - -- + ------------------- <= 0| ||- --- + -- + -------------- for - --- + -- + ------------------- >= 0|
I*im|< 121 11 121 121 11 121 | + I*im|< 121 11 121 121 11 121 | + I*im|< 121 121 11 121 11 121 | + I*im|< 121 11 121 121 11 121 | + re|< 121 11 121 121 11 121 | + re|< 121 11 121 121 11 121 | + re|< 121 121 11 121 11 121 | + re|< 121 11 121 121 11 121 |
|| | || | || | || | || | || | || | || |
|| nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise | || nan otherwise |
\\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ /
$$\operatorname{re}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$
product
/ // ____________ ___ ___________ \ // ____________ ___ ___________ \\ / // ____________ ___ ___________ \ // ____________ ___ ___________ \\ / // ____________ ___ ___________ \ // ____________ ___ ___________ \\ / // ____________ ___ ___________ \ // ____________ ___ ___________ \\ | || 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a | || 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a || | || 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a | || 1 a \/ 122 + 22*a 1 a \/ 2 *\/ 61 + 11*a || | || 1 \/ 122 - 22*a a 1 a \/ 2 *\/ 61 - 11*a | || 1 \/ 122 - 22*a a 1 a \/ 2 *\/ 61 - 11*a || | || 1 a \/ 122 - 22*a 1 a \/ 2 *\/ 61 - 11*a | || 1 a \/ 122 - 22*a 1 a \/ 2 *\/ 61 - 11*a || | ||- --- - -- - -------------- for --- + -- + ------------------- > 0| ||- --- - -- - -------------- for --- + -- + ------------------- > 0|| | ||- --- - -- + -------------- for --- + -- - ------------------- > 0| ||- --- - -- + -------------- for --- + -- - ------------------- > 0|| | ||- --- - -------------- + -- for --- - -- + ------------------- <= 0| ||- --- - -------------- + -- for --- - -- + ------------------- <= 0|| | ||- --- + -- + -------------- for - --- + -- + ------------------- >= 0| ||- --- + -- + -------------- for - --- + -- + ------------------- >= 0|| |I*im|< 121 11 121 121 11 121 | + re|< 121 11 121 121 11 121 ||*|I*im|< 121 11 121 121 11 121 | + re|< 121 11 121 121 11 121 ||*|I*im|< 121 121 11 121 11 121 | + re|< 121 121 11 121 11 121 ||*|I*im|< 121 11 121 121 11 121 | + re|< 121 11 121 121 11 121 || | || | || || | || | || || | || | || || | || | || || | || nan otherwise | || nan otherwise || | || nan otherwise | || nan otherwise || | || nan otherwise | || nan otherwise || | || nan otherwise | || nan otherwise || \ \\ / \\ // \ \\ / \\ // \ \\ / \\ // \ \\ / \\ //
$$\left(\operatorname{re}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} - \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - \frac{a}{11} + \frac{\sqrt{22 a + 122}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} - \frac{\sqrt{2} \sqrt{11 a + 61}}{121} + \frac{1}{121} > 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} - \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: - \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} + \frac{1}{121} \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \frac{a}{11} + \frac{\sqrt{122 - 22 a}}{121} - \frac{1}{121} & \text{for}\: \frac{a}{11} + \frac{\sqrt{2} \sqrt{61 - 11 a}}{121} - \frac{1}{121} \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$
=
/ 4 4 2 2 2 2 3 3 |1 + im (a) + re (a) - 2*re (a) + 2*im (a) - 6*im (a)*re (a) - 4*I*im (a)*re(a) - 4*I*im(a)*re(a) + 4*I*re (a)*im(a) / 61 \ |------------------------------------------------------------------------------------------------------------------- for And|a <= --, a > 1| < 14641 \ 11 / | | nan otherwise \
$$\begin{cases} \frac{\left(\operatorname{re}{\left(a\right)}\right)^{4} + 4 i \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 i \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 i \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 1}{14641} & \text{for}\: a \leq \frac{61}{11} \wedge a > 1 \\\text{NaN} & \text{otherwise} \end{cases}$$
Piecewise(((1 + im(a)^4 + re(a)^4 - 2*re(a)^2 + 2*im(a)^2 - 6*im(a)^2*re(a)^2 - 4*i*im(a)^3*re(a) - 4*i*im(a)*re(a) + 4*i*re(a)^3*im(a))/14641, (a <= 61/11)∧(a > 1)), (nan, True))