Question

Convert the complex number 2 - 2 (sqrt 3) i into its polar representation.

Answer 1

2 sqrt 2(cos(240) + isin(240))

-4(cos(120) + isin(120))

4(cos(300) + isin(300))

4 sqrt 3(cos(60) + isin(60))

Answer 2

I don't even know where to start...

Answer 3

\[\Large\rm z=2-2\sqrt3~\mathcal i\]
We can write our point in polar form:\[\Large\rm z=r(\cos \theta+\mathcal i \sin \theta)\]By figuring out the \(\Large\rm r\) and \(\Large\rm \theta\).

Answer 4

When we have a point of the form:
\[\Large\rm z=a+b\mathcal i\]The radius is given by:\[\Large\rm r=\sqrt{a^2+b^2}\]And theta is given by:\[\Large\rm \tan \theta=\frac{b}{a}\qquad\to\qquad \theta=\arctan \frac{b}{a}\]

Answer 5

So what is our radius in this case?\[\Large\rm r=\sqrt{2^2+\left(-2\sqrt3\right)^2}\]