Complex Numbers More like Complicated Math

Question

Change the complex number, 1 - i square root 3, to polar form. Find the exact answer.

Answer 1

1-i√3

√(1^2+√3^2)

√(1+3

√4=2

r=2

tanθ=-√3/1=-√3

θ=tan^-1(-√3)

θ=-60°

2(cos(-60°)+isin(-60°))

2(cos60°-isin60°)

Answer 2

To convert the complex number √3(1-i)=√3-√3i to the polar form r[cos(θ)+isin(θ)] we need to find out how far away this number is located from the origin (r) and what angle it makes with the positive x axis (θ).

r=√[(√3)²+(-√3)²]=√(3+3)=√6

θ=tan^-1(-√3/√3)=tan^-1(-1)=-π/4

It follows that the polar form of this complex number is:

√6[cos(-π/4)+isin(-π/4)]