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Complex Numbers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers1 Mark
MCQ
The principal value of the amplitude of (1 + i) is:
  • ✓
    $\frac{\pi}{4}$
  • B
    $\frac{\pi}{12}$
  • C
    $\frac{3\pi}{4}$
  • D
    $\pi$
✓

Answer

Correct option: A.
$\frac{\pi}{4}$
  1. $\frac{\pi}{4}$
​​​​​​​Solution:
Let $\text{z}=(1+\text{i})$
$\Rightarrow\tan\alpha=\Big|\frac{\text{Im(z)}}{\text{Re(z)}}\Big|$
$=1$
$\Rightarrow\alpha=\frac{\pi}{4}$
Since, z lies in the first quadrant.
Therefore, $\text{arg(z)}=\frac{\pi}{4}$

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