Expert: Ahmed Salami - 7/28/2010

Question
Convert the given complex number in rectangular form to polar form
-√3+i

Thank you for your time.

Answer
Hi Travis,
The complex number z = x + iy is written in polar form as z = re^(iθ)
where
r = √(x² + y²)
θ = arctan(y/x)
OR
θ = π + arctan(y/x)  (when x < 0)
So, for -√3 + i
x = -√3
y = 1

r = √((-√3)² + 1²)
 = √(3 + 1) = √4 = 2

θ = π + arctan(1/-√3)  (since x < 0)
 = π + (-π/6)
 = 5π/6

Therefore,
-√3 + i = 2e^(5πi/6)

Regards