Complex Numbers
Number of solutions of complex equation
Grade Class 12
Question:
Number of complex numbers satisfying the equation $z^2 = \bar{z}\cdot 2^{1-k}$ is
Step-by-Step Solution
Key Concept: Write $z=re^{i\theta}$. The equation $z^2=\bar{z}\cdot2^{1-k}$ becomes $r^2e^{2i\theta}=re^{-i\theta}\cdot2^{1-k}$. Separate modulus and argument.
3 complex numbers (including $z=0$).
Correct Answer: 3