Question

Please help me fast

Complex number question

Answer 1

The number of non zero values of z such that conjugate of z = z^4 is
(a) 5
(b) 6
(c) 8
(d) 9

Answer 2

Please help me

Answer 3

Let
\[z= re^{i\theta}\]
It's given conjugate of z is equal to z^4
so
\[re^{-i\theta}=r^4e^{4 i\theta}\]
We can see that both will be equal if r=1
so
\[e^{-i\theta}=e^{4i\theta}\]
so
\[\cos \theta+i\sin \theta=\cos 4\theta-i\sin 4\theta\]
Equate real and imaginary parts
\[\cos \theta= \cos 4\theta\]
\[\sin \theta=-\sin 4\theta\]
Can you solve now?

Answer 4

Thanks a lot

Answer 5

But then there will exist a large number of values , if i m right.

Answer 6

Yeah you'll get numerous solutions

Answer 7

Can u please tell me the exact number of solutions.....please