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  • z and w are two non zero complex number such that | z | = | w | and Arg z + Arg w =  then z equals<div class='qn

z and w are two non zero complex number such that | z | = | w | and Arg z + Arg w = \pi then z equals

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Answers (1)

best_answer

|z|=|\omega|=r\;\;(say)

Let \omega =re^{i\theta} then \bar\omega =re^{-i\theta}

\arg (z)+\arg(\omega )=\pi

\arg (z)=\pi-\arg(\omega )

z=re^{i(\pi-\theta)}

z=e^{i\pi}\cdot re^{-i\theta}

z=r(\cos \pi+i\sin\pi)e^{-i\theta}

z=r(-1+0)e^{-i\theta}

z=-re^{-i\theta}

z=-\bar\omega

 

Posted by

avinash.dongre

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