What is the principal value of amplitude of \(\rm \sqrt{3}\) - i ?

Question

Question

Answer 1

Concept:

when z = x + iy then, Principal amplitude of a complex number, θ = tan^-1(\(\rm \frac{y}{x}\))

tan \(\rm \frac{\pi }{6}\) = \(\rm \frac{1}{{\sqrt{3}}}\)

x > 0, y < 0, The point lies in IVth quadrant.

Calculation:

Let θ be the principal value of amplitude of \(\rm \sqrt{3}\) - i

Since, tan θ = \(\rm \frac{-1}{{\sqrt{3}}}\) and \(\rm \sqrt{3}\) - i lies in IV^thquadrant.

tan θ = tan (-\(\rm \frac{\pi }{6}\)), θ = -\(\rm \frac{\pi }{6}\)