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Mathematics 10 Online
OpenStudy (vishweshshrimali5):

Please help me fast Complex number question

OpenStudy (vishweshshrimali5):

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

OpenStudy (vishweshshrimali5):

Please help me

OpenStudy (vishweshshrimali5):

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OpenStudy (ash2326):

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?

OpenStudy (vishweshshrimali5):

Thanks a lot

OpenStudy (vishweshshrimali5):

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

OpenStudy (ash2326):

Yeah you'll get numerous solutions

OpenStudy (vishweshshrimali5):

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

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