Question

Convert -(3)^1/2 - i to polar form

Answer 1

2(cos30°+isin30°)

Explanation:

Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.

On converting the rectangluar to polar form of the complex number;

x = rcosθ and y = rsinθ

Substituting in the rectangular form of the comlex number above;

z = rcosθ + irsinθ

z = r(cosθ+isinθ)

r is the modulus of the complex number and θ is the argument

r =√x²+y² and θ = tan⁻¹y/x

Given the complex number in rectangular form z = -(3)^1/2 - i

z = -√3 - i

x = -√3 and y = -1

r = √(-√3)²+(-1)²

r = √3+1

r = √4

r = 2

θ = tan⁻¹ (-1/-√3)

θ = tan⁻¹ (1/√3)

θ = 30°

Hence the complex number in polar form will be z = 2(cos30°+isin30°)