Question

47. Find the possible no. of solutions of z^2=z bar where z belongs to complex numbers. ​

Answer 1

Answer:

Step-by-step explanation:

z2=z

to find the no. of solution of z2=z

Solution:-

Given equation,

z2=z

Taking modulus both sides we get

∣z∣2=∣z∣{∣z∣=∣z∣}

∣z∣2=∣z∣

So,∣z∣=0,1

case(1),∣z∣=0,z=0

case(2),∣z∣=1,

Then the equation is

z2=z=z−1

z3=1

This gives the remaining 3 solution.

Hence, the no. of solution of equationz2=z