Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+2x+1=0
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Equation cos(x)+1=0
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Equation (x+10)2=(5-x)2
- Equation x^2-cos(n*x)*x^2+6*x+9=0
- Express {x} in terms of y where:
- -4*x+4*y=-5
- -11*x+8*y=0
- -2*x-9*y=16
- -12*x-14*y=20
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Identical expressions
- -i2sinz-cosz= five
- minus i2 sinus of z minus co sinus of e of z equally 5
- minus i2 sinus of z minus co sinus of e of z equally five
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Similar expressions
- i2sinz-cosz=5
- -i2sinz+cosz=5
-i2sinz-cosz=5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
-i2*sin(z) - cos(z) = 5
$$- i_{2} \sin{\left(z \right)} - \cos{\left(z \right)} = 5$$
The graph
Sum and product of roots
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sum
/ / ___________ \\ / / ___________ \\ / / ___________\\ / / ___________\\
| | / 2 || | | / 2 || | | / 2 || | | / 2 ||
| | \/ -24 + i2 i2|| | | \/ -24 + i2 i2|| | |i2 \/ -24 + i2 || | |i2 \/ -24 + i2 ||
- 2*re|atan|- -------------- + --|| - 2*I*im|atan|- -------------- + --|| + - 2*re|atan|-- + --------------|| - 2*I*im|atan|-- + --------------||
\ \ 4 4 // \ \ 4 4 // \ \4 4 // \ \4 4 //
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} - \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} - \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} + \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} + \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)}\right)$$
=
/ / ___________ \\ / / ___________\\ / / ___________ \\ / / ___________\\
| | / 2 || | | / 2 || | | / 2 || | | / 2 ||
| | \/ -24 + i2 i2|| | |i2 \/ -24 + i2 || | | \/ -24 + i2 i2|| | |i2 \/ -24 + i2 ||
- 2*re|atan|- -------------- + --|| - 2*re|atan|-- + --------------|| - 2*I*im|atan|- -------------- + --|| - 2*I*im|atan|-- + --------------||
\ \ 4 4 // \ \4 4 // \ \ 4 4 // \ \4 4 //
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} - \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} + \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} - \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} + \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)}$$
product
/ / / ___________ \\ / / ___________ \\\ / / / ___________\\ / / ___________\\\ | | | / 2 || | | / 2 ||| | | | / 2 || | | / 2 ||| | | | \/ -24 + i2 i2|| | | \/ -24 + i2 i2||| | | |i2 \/ -24 + i2 || | |i2 \/ -24 + i2 ||| |- 2*re|atan|- -------------- + --|| - 2*I*im|atan|- -------------- + --|||*|- 2*re|atan|-- + --------------|| - 2*I*im|atan|-- + --------------||| \ \ \ 4 4 // \ \ 4 4 /// \ \ \4 4 // \ \4 4 ///
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} - \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} - \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} + \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} + \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)}\right)$$
=
/ / / ___________ \\ / / ___________ \\\ / / / ___________\\ / / ___________\\\ | | | / 2 || | | / 2 ||| | | | / 2 || | | / 2 ||| | | | \/ -24 + i2 i2|| | | \/ -24 + i2 i2||| | | |i2 \/ -24 + i2 || | |i2 \/ -24 + i2 ||| 4*|I*im|atan|- -------------- + --|| + re|atan|- -------------- + --|||*|I*im|atan|-- + --------------|| + re|atan|-- + --------------||| \ \ \ 4 4 // \ \ 4 4 /// \ \ \4 4 // \ \4 4 ///
$$4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} - \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} - \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} + \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} + \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)}\right)$$
4*(i*im(atan(-sqrt(-24 + i2^2)/4 + i2/4)) + re(atan(-sqrt(-24 + i2^2)/4 + i2/4)))*(i*im(atan(i2/4 + sqrt(-24 + i2^2)/4)) + re(atan(i2/4 + sqrt(-24 + i2^2)/4)))
Rapid solution
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/ / ___________ \\ / / ___________ \\
| | / 2 || | | / 2 ||
| | \/ -24 + i2 i2|| | | \/ -24 + i2 i2||
z1 = - 2*re|atan|- -------------- + --|| - 2*I*im|atan|- -------------- + --||
\ \ 4 4 // \ \ 4 4 //
$$z_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} - \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} - \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)}$$
/ / ___________\\ / / ___________\\
| | / 2 || | | / 2 ||
| |i2 \/ -24 + i2 || | |i2 \/ -24 + i2 ||
z2 = - 2*re|atan|-- + --------------|| - 2*I*im|atan|-- + --------------||
\ \4 4 // \ \4 4 //
$$z_{2} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} + \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{i_{2}}{4} + \frac{\sqrt{i_{2}^{2} - 24}}{4} \right)}\right)}$$
z2 = -2*re(atan(i2/4 + sqrt(i2^2 - 24)/4)) - 2*i*im(atan(i2/4 + sqrt(i2^2 - 24)/4))