Question

If $0 < \alpha

• A. clockwise rotation around origin through an angle $\alpha$
• B. anti-clockwise rotation around origin through an angle $\alpha$
• C. reflection in the line through origin with slope tan $\alpha$
• D. reflection in the line through origin with slope tan $\frac{\alpha}{2}$

Answer 1

Answer: (D)

reflection in the line through origin with slope tan $\frac{\alpha}{2}$

Answer 2

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 $\alpha / 2$