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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$\frac{\pi}{2}$

Vedclass · Answer

(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

Similar Questions

If $w = \frac{z}{z - \frac{1}{3}i}$ and $|w| = 1$,where $i = \sqrt{-1}$,then $z$ lies on

If $z = x + iy$ and $\omega = \frac{1 - iz}{z - i}$,then $|\omega| = 1$ shows that in the complex plane:

The equation $\overline{b}z + b\overline{z} = c$,where $b$ is a non-zero complex constant and $c$ is real,represents:

The locus of $z$ given by $\left| \frac{z - 1}{z - i} \right| = 1$ is

In the Argand plane,the vector $z = 4 - 3i$ is turned in the clockwise sense through $180^o$ and stretched three times. The complex number represented by the new vector is

Vedclass Test Series

Exam Paper Generator

Online Exam Module