Question

 Find all non-zero complex numbers z satisfying z iz².

Answer 1

Z = i(Z² )⇒ Let x = a + ib 

a – ib = i(a² – b² + 2abi) 

⇒ a = –2ab and –b = a² – b² 

a(1 + 2b) = 0 and a² = b² – b

a = 0 or b = -1/2

if a = 0 ⇒ b = 0, 1 

if b = -1/2, a = ±√3/2.

complex numbers are z = 0, i ± √3/2 -i/2