The centre of a regular polygon of n sides is | vedclass

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(A) Let $O$ be the origin $(z=0)$ and $A$ be the vertex with affix $z_1$. Since it is a regular polygon of $n$ sides,the angle subtended by any side a

Vedclass · Accepted Answer

$z_1 \left( \cos \frac{2\pi}{n} \pm i \sin \frac{2\pi}{n} \right)$

Vedclass · Answer

(A) Let $O$ be the origin $(z=0)$ and $A$ be the vertex with affix $z_1$. Since it is a regular polygon of $n$ sides,the angle subtended by any side at the centre is $\frac{2\pi}{n}$.$z_2$ can be obtained by rotating $z_1$ about the origin through an angle of $\pm \frac{2\pi}{n}$.Using the rotation formula,$z_2 = z_1 e^{\pm i \frac{2\pi}{n}}$.Applying Euler's formula,$z_2 = z_1 \left( \cos \frac{2\pi}{n} \pm i \sin \frac{2\pi}{n} \right)$.

The centre of a regular polygon of $n$ sides is located at the point $z = 0$ and one of its vertices $z_1$ is known. If $z_2$ is the vertex adjacent to $z_1$,then $z_2$ is equal to

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