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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
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
  • B
    -1 - 2i
  • C
    2 + i
  • D
    -1 + 2i
✓

Answer

  1. -1 - 2i

Solution:

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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