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Complex Numbers and Quadratic Equations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers and Quadratic Equations1 Mark
MCQ
The argument of every complex number is:
  • A
    Double valued
  • B
    Single valued
  • C
    Many valued
  • D
    Triple valued
✓

Answer

  1. Many valued

Solutions:

z = x + iy

amplitude $=\tan^{-1}\frac{\text{y}}{\text{x}}$

⇒ amplitude $=\theta\pm2\text{k}\pi$ where $\theta\in[-\pi,\pi]\ \forall\text{k}\in\text{R}$

since $\text{k}\in\text{R}$

⇒ Amplitude of any complex number is many valued.

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