Question

Find all non-zero complex numbers satisfying (bar)Z  = i = Z²

Answer 1

Therefore, the equation is

x − iy = i (x² - y² + 2ixy)

Equating real and imaginary parts, we get

x = -2xy

-y = x² - y²

Equation (1) gives either x = 0, in that case y = 0 ; y = 1, or

y = -1/2, in that case 1/4 + 1/2 = x²

Therefore, 

Hence, the non-zero Z, satisfying the equation are