Question:
Find the modulus of each of the following complex numbers and hence express each of them in polar form: $\left(\sin 120^{\circ}-i \cos 120^{\circ}\right)$
Solution:
= sin(90° + 30° ) - icos(90° + 30°)
$=\cos 30^{\circ}+i \sin 30^{\circ}$
Since, sin(90°+ α) = cosα
And cos(90° + α) = -sinα
$=\frac{\sqrt{3}}{2}+i \frac{1}{2}$
Hence it is of the form
$\mathrm{Z}=\frac{\sqrt{3}}{2}+i \frac{1}{2}=\mathrm{r}(\cos \theta+i \sin \theta)$
Therefore r = 1
Hence its modulus is 1 and argument is $\frac{\pi}{6}$.