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Concept of rotation - Rotation of complex Number about origin

Concept of rotation

Best iitjee maths for mains and advance
Rotation from Z1 to Z2
Rotation about origin O from A ($Z_1$) to B($Z_2$).

Concept of RotationAs multiplying a complex number by $e^{i\alpha}$

Let $Z = r.e^{i\theta}$ is a non zero complex number where $r=\vert Z \vert $ and $\theta = arg(Z)$.

$\therefore$ when we multiply $e^{i\alpha}$ to Z we get a complex number Say $W=Ze^{i\alpha}=r.e^{i(\alpha + \theta)}$

$\therefore$ Geometrically $Z.e^{i\alpha} = W$ can be obtained by rotating OA in anticlockwise direction by an angle $\alpha $ , which is also called as the concept of rotation .


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