Question

The equation solution $z^2=\overline{z}$ where z is a complex number has

• A. 4 solution
• B. 2 solution
• C. no solution
• D. infinitely many solutions

Answer 1

The correct option is A 4 solution

Given:-

$z^2=\overline{z}$

to find the no. of solution of $z^2=\overline{z}$

Solution:-

Given equation,

$z^2=\overline{z}$

Taking modulus both sides we get

${\left|z\right|}^2=\left|\overline{z}\right|\{\left|\overline{z}\right|=\left|z\right|\}$

${\left|z\right|}^2=\left|z\right|$

So,$\left|z\right|=0,1$

case$\left(1\right),\left|z\right|=0,z=0$

case$\left(2\right),\left|z\right|=1$,

Then the equation is

$z^2=\overline{z}=z^{-1}$

$z^3=1$

This gives the remaining $3$ solution.

Hence, the no. of solution of equation$z^2=\overline{z}$ is $4$ solution.