Two complex numbers are given by $z=2+2i$ and $\omega=i$. Express $z$ and $\omega$ in expone

Question

Two complex numbers are given by $z=2+2i$ and $\omega=i$. Express $z$ and $\omega$ in exponential form. Hence, (i) find $z\omega$ in exponential form, (ii) describe the transformation that takes place when $z$ is multiplied by $\omega$.

Accepted Answer

(a) $z=2\sqrt2\,e^{i\pi/4},\ \omega=e^{i\pi/2}$ (b)(i) $z\omega=2\sqrt2\,e^{i3\pi/4}$ (b)(ii) Anticlockwise rotation through $\frac{\pi}{2}$ about the origin.

Multiplication as a rotation of the complex plane

Multiplication as a rotation of the complex plane

Solution:

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