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

  1. -π/3
  2. π/6
  3. π/3
  4. -π/6

Answer (Detailed Solution Below)

Option 4 : -π/6
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Detailed Solution

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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 IVth quadrant.

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

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