In the Argand diagram,if O, P and Q represent | vedclass

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(C) Let the origin $O$ be represented by $0$. Let the point $P$ be represented by the complex number $z$. Let the point $Q$ be represented by the comp

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$\frac{\pi}{2}$

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(C) Let the origin $O$ be represented by $0$. Let the point $P$ be represented by the complex number $z$. Let the point $Q$ be represented by the complex number $z + iz$. The vector $\vec{OP}$ corresponds to the complex number $z - 0 = z$. The vector $\vec{PQ}$ corresponds to the complex number $(z + iz) - z = iz$. We know that multiplying a complex number by $i$ corresponds to a rotation of $90^\circ$ or $\frac{\pi}{2}$ radians in the counter-clockwise direction. Since $\vec{PQ} = i \vec{OP}$,the vector $\vec{PQ}$ is perpendicular to $\vec{OP}$. Therefore,the angle $\angle OPQ$ is $\frac{\pi}{2}$.

In the Argand diagram,if $O, P$ and $Q$ represent the origin,the complex number $z$ and the complex number $z + iz$ respectively,then the angle $\angle OPQ$ is

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