Question

Convert the following complex number into its polar repersentation of -4i

Answer 1

As we know that any complex number written in the form $a+ib$

can also be written as $(a,b)$ in the complex plane.

Here the given complex number is $-4i$

which can be written as $0-4i \ or \ (0,-4)$

The polar representation is given as $z=re^{i \theta}$

$r=\sqrt{4^2+0^2}=4\\ \\ \theta=tan^{-1 }\frac{-4}{0} =\infty\\ \\ \theta=\pi/2$

Hence the polar representation is

$z=4e^{i \frac{\pi }{2} }$