Question

The imaginary part of $\frac{\cos 50^{\circ}+i\sin 50^{\circ}}{\cos 50^{\circ}-i\sin 50^{\circ}}$ is equal to

• A. $\cos 10^{\circ}$
• B. $\sin 80^{\circ}$
• C. $\cos 50^{\circ}$
• D. $\sin 40^{\circ}$
• E. $\cos 40^{\circ}$

Hint:

Logic Tip: When dividing complex numbers in the format $\frac{z}{\bar{z}}$, the result is always $e^{i(2\theta)}$. Here, $\theta = 50^{\circ}$, so the result is immediately $e^{i 100^{\circ}}$.

Answer 1

The Correct Option is A