Question

What is the polar form of -3+root3i?

Answer 1

Compute the modulus and argument:

|-3 + √3 i| = √((-3)² + (√3)²) = √12 = 2√3

arg(-3 + √3 i) = π - arg(3 + √3 i)

… = π - arctan(√3/3)

… = π - arctan(1/√3)

… = π - π/6

… = 5π/6

So, the polar form is

-3 + √3 i = 2√3 (cos(5π/6) + i sin(5π/6))