Question

Convert the complex number 2-2√3i into its polar representation.

Answer 1

There is a more accurate way to solve these using arctangent and finding the magnitude of the complex value...
but I like to do these a little weirder.
\[\Large\rm 2-2\sqrt3 ~i\]If we pull a 4 out of each term, we can create these special trig values that we often see,

Answer 2

\[\Large\rm =4\left(\frac{1}{2}-\frac{\sqrt3}{2}~i\right)\]

Answer 3

And then think about which angle gives you:\[\Large\rm \cos \theta=\frac{1}{2}\]\[\Large\rm \sin \theta=-\frac{\sqrt3}{2}\]

Answer 4

If cosine is positive,
and sine is negative,

which quadrant are we in?

Answer 5

4

Answer 6

Mm ya good :)

Answer 7

Can you figure out which angle it is? :U

Answer 8

@zepdrix is that choice b.

Answer 9

yay good job \c:/