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COMPLEX NUMBERS AND QUADRATIC EQUATIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSCOMPLEX NUMBERS AND QUADRATIC EQUATIONS1 Mark
MCQ
The argument of every complex number is:
  • A
    Double valued
  • B
    Single valued
  • ✓
    Many valued
  • D
    Triple valued
✓

Answer

Correct option: C.
Many valued
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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