Question:
If $0 < \alpha
If $0 < \alpha
Updated On: Jun 14, 2022
- clockwise rotation around origin through an angle $\alpha$
- anti-clockwise rotation around origin through an angle $\alpha$
- reflection in the line through origin with slope tan $\alpha$
- reflection in the line through origin with slope tan $\frac{\alpha}{2}$
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The Correct Option is D
Solution and Explanation
In the Argand plane, P is represented by e$^{io}$ and Q is
represented by e$^i{(\alpha-\theta)}$
Now, rotation about a line with angle a is given by
$\, e^\theta \rightarrow e^{(\alpha-\theta)}$ Therefore, Q is obtained from P by reflection
in the line making an angle $\alpha / 2$
represented by e$^i{(\alpha-\theta)}$
Now, rotation about a line with angle a is given by
$\, e^\theta \rightarrow e^{(\alpha-\theta)}$ Therefore, Q is obtained from P by reflection
in the line making an angle $\alpha / 2$
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Concepts Used:
Argand Plane
It is a set of 3 mutually perpendicular axes and a convenient way to represent a set of numbers (2 or 3) or a point in space.
Hence, we have a way to represent an imaginary number graphically. All we need to do is to find the real part and an imaginary part of it. Then, represent them on the two mutually perpendicular number lines. The point of intersection, as shown in the above diagram, is the origin of our Plane.
The formation of the Plane so formed is known as the Argand Plane and it is a convenient way to represent an imaginary number graphically.