Question

The number of solutions of z³ + $\bar{z}$ = 0 is

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (D)

5

Answer 2

Sol. z³ = –$\bar{z}$Ž |z|³ = | –$\bar{z}$| or |z|³ = |z| Ž |z| = 0 or |z| = 1

|z| = 0 Ž z = 0 also |z| = 1. Let z = cosq + isinq

then equation becomes cos3q + isin3q + cosq – isinq = 0

Ž cos3q + cosq = 0 & sin3q = sinq