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  4. The principal argument of the complex number z=(1+ sin π- cos π/1+ sin π+i cos π) is

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Q. The principal argument of the complex number $z=\frac{1+\sin \pi-\cos \pi}{1+\sin \pi+i \cos \pi}$ is

KEAMKEAM 2020

Solution:

$z=\frac{1+i}{1-i}=i$
$\Rightarrow \arg (z)=\frac{\pi}{2}$