Question

How do you write 1-2i in polar form?

Answer 1

Polar form: a+bi = r(cos(θ)+isinθ).
You need r and θ for the polar form.

r=√(a²+b²)
θ = arctan(b/a)

So if you use a=1 and b=-2 in these formulas,
you can put them in the polar form r(cos(θ)+isinθ).

Answer 2

the arctan produces an angle of -63.4. However, when I use the formula x=rcos(theta), I get an angle of +63.4 and 296.6. I'm not sure which angle to use.

Answer 3

If you put 1-2i in the complex plane, you'll see that is is in the fourth quadrant, so the angle is -63.4.