Complex Numbers-Converting Rectangular to Polar

Question

Hi everyone, I have a question about converting rectangular to polar. I cant seem to find an answer online.

When there are no negatives, or when the imaginary number is negative, to get the angle it is simply tan-1 imaginary/real.

But.. when the real number is negative, I am not getting the correct answers. If anyone knows what to do differently when the real number is negative please let me know.

Thanks

Answer 1

Think of the different quadrants of a circle. When the real part is negative, where is the point on the complex plane? What should the argument of the polar coordinate be?

Answer 2

Instead of looking at the complex plane, let's just look at the unit circle

What is the angle for the point (1/2, sqrt(3)/2)?

How about the angle (-1/2, -sqrt(3)/2)?

How do these two angles relate?

Can you see how this might be analogous to the complex plane?