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If $z\neq 0$ is a complex no having arg=$\large\frac{\pi}{4}$,then

$\begin{array}{1 1}(A)Re (z^2)=0 \\ (B) Im(z^2)=0 \\ (C) Re(z^2)=Im(z^2) \\(D) None\;of\;these \end{array}$

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1 Answer

arg(z)=$\large\frac{\pi}{4}$
$\Rightarrow z=r(\cos\large\frac{\pi}{4}$$+i\sin \large\frac{\pi}{4})$
$z^2=r^2(\cos\large\frac{\pi}{2}+$$i\sin\large\frac{\pi}{2})$
(By De Moivre's theorem)
$\Rightarrow z^2=r^2(0+i)$
$\Rightarrow Re(z^2)=0$
Hence (A) is the correct answer.
answered Apr 9, 2014 by sreemathi.v
 

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