Let z,wbe complex numbers such that overline | vedclass

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Question

(c)Given that arg zw =$\pi $ .....$(i)$
$\bar z + i\bar \omega = 0 \Rightarrow \bar z = - i\bar \omega $$ \Rightarrow z = i\omega $$ \Rightarrow \ome

Vedclass · Accepted Answer

$3\pi /4$

Vedclass · Answer

(c)Given that arg zw =$\pi $ .....$(i)$
$\bar z + i\bar \omega = 0 \Rightarrow \bar z = - i\bar \omega $$ \Rightarrow z = i\omega $$ \Rightarrow \omega = - iz$
From $(i)$, arg$( - i{z^2}) = \pi $
$arg\;( - i) + 2arg(z) = \pi $ ;

$\frac{{ - \pi }}{2} + 2\;arg(z) = \pi $
$2\,arg\,(z) = \frac{{3\pi }}{2}$;

$a\,rg(z) = \frac{{3\pi }}{4}$

Let $z,w$be complex numbers such that $\overline z + i\overline w = 0$and $arg\,\,zw = \pi $. Then arg z equals

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