Question

The equation z² = $\bar{z}$ has –

• A. No solution
• B. 2 solutions
• C. Four solutions
• D. An infinite number of solutions

Answer 1

Answer: (C)

Four solutions

Answer 2

Sol. $\begin{matrix} z^{2} = \bar{z} \end{matrix}$ Ž ($\bar{z}$)² = $\overline{z}$Ž (z²)² = z Ž $\begin{matrix} z^{4} = z \end{matrix}$

z = 0 or z³ = 1 Ž $\begin{matrix} z = 0,1,\omega,\omega^{2} \end{matrix}$

Hence four solutions.