As we know that any complex number written in the form [tex] a+ib [/tex]
can also be written as [tex] (a,b) [/tex] in the complex plane.
Here the given complex number is [tex] -4i [/tex]
which can be written as [tex] 0-4i \ or \ (0,-4) [/tex]
The polar representation is given as [tex] z=re^{i \theta} [/tex]
[tex] r=\sqrt{4^2+0^2}=4\\
\\
\theta=tan^{-1 }\frac{-4}{0} =\infty\\
\\
\theta=\pi/2 [/tex]
Hence the polar representation is
[tex] z=4e^{i \frac{\pi }{2} } [/tex]
