Download App

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 $=\text{z}\cdot\text{e}^{-\big(\frac{\pi}{2}\big)}$

$=(2-\text{i})\text{e}^{-\big(\frac{\pi}{2}\big)}$

$=(2-\text{i})\Big[\cos\Big(\frac{-\pi}{2}\Big)+\text{i}\sin\Big(\frac{-\pi}{2}\Big)\Big]$

$=(2-\text{i})(0-\text{i})$

$=-1-2\text{i}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Complex Numbers and Quadratic Equations→Complex Numbers and Quadratic Equations — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

If sets A and B are defined as $\text{A}=\Big\{(\text{x},\text{y})|\text{y}=\frac{1}{\text{x}},0\neq\text{x}\in\text{R}\Big\}\ \text{B}=\{(\text{x},\text{y})|\text{y}=-\text{x},\text{x}\in\text{R}\},$ then

  1. $\text{A}\cap\text{B}=\text{A}$

  2. $\text{A}\cap\text{B}=\text{B}$

  3. $\text{A}\cap\text{B}=\phi$

  4. $\text{A}\cup\text{B}=\text{A}$

→
If A = {1, 2, 3, 4, 5, 6} then the number of proper subsets is
→
If the difference between the roots of the equation $\text{x}^2 +\text{ax}+1=0$ is less than $\sqrt{5},$ then the set of possible values of a is:
→
If G is centroid of $\triangle\text{ABC}$ then:
→
If $\text{f(x)} = \sin^{2}\text{x}$ and the composite function $ \text{g}{\text{f(x)}} = | \sin\text{ x } |$, then the function g(x) is equal to:
→
If R is a relation on a finite set having n elements, then the number of relations on A is:
  1. $2^{\text{n}}$
  2. $2^{\text{n}^2}$
  3. $\text{n}^2$
  4. $\text{n}^\text{n}$
→
The amplitude of $\frac{1}{\text{i}}$ is equal to:
→
If $1,\omega ,{{\omega }^{2}}$ are the cube roots of unity, then their product is [Karnataka CET 1999, 2001]
→
The common ratio of geometric progression $\sqrt{3}, \frac{1}{\sqrt{3}}, \frac{1}{3 \sqrt{3}}, \ldots \ldots$ is :
→

If p be the length of the perpendicular from the origin on the line $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1,$ then:

→