Question

Express the complex number $\frac{-3}{2}+\frac{3\sqrt{3}}{2}i$ polar form.

Answer 1

Answer:

Polar form is 3e^(-iπ/3)

Step-by-step explanation:

Hi,

If z = a + ib is a complex number , then its polar form

is given by z = r.e^(iθ),

where r = √a² + b² and

θ = tan⁻¹(b/a)

Consider -3/2 + (3√3/2)i

Here a = 3/2 and b = 3√3/2

r = √(3/2)² + (3√3/2)²

= √9/4 + 27/4

= √36/4

= √9

= 3

θ = tan⁻¹(b/a)

= tan⁻¹( (3√3/2)/(-3/2))

= tan⁻¹(-√3)

= -π/3

Hence, polar form is 3e^(-iπ/3)

Hope, it helps !