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

CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers and Quadratic Equations1 Mark
MCQ
Choose the correct answer.
The point represented by the complex number $2 - i$ is rotated about origin through an angle $\frac{\pi}{2}$ in the clockwise direction, the new position of point is:
  • A
    $1 + 2i$
  • ✓
    $-1 - 2i$
  • C
    $2 + i$
  • D
    $-1 + 2i$
✓

Answer

Correct option: B.
$-1 - 2i$
Given that, $\text{z}=2-\text{i}$
If $z$ rotated through an angle of $\frac{\pi}{2}$ about the origin in clockwise direction.
Then the new position $=\text{z}\cdot\text{e}^{-\big(\frac{\pi}{2}\big)}$
$=(2-\text{i})\text{e}^{-\big(\frac{\pi}{2}\big)}$
$=(2-\text{i})\Big[\cos\Big(\frac{-\pi}{2}\Big)+\text{i}\sin\Big(\frac{-\pi}{2}\Big)\Big]$
$=(2-\text{i})(0-\text{i})$
$=-1-2\text{i}$

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