\((a+bi)^2=2(a-bi)\)
(a + bi)^2 = 2( a - bi)
a^2 + 2abi - b^2 = 2a - 2bi
Equating the real and imaginary parts, we have that
(a^2 - b^2) = 2a 2abi = - 2bi
Using the second equation
2a = -2
a = -1
And using the first equation
(-1)^2 - b^2 = -2
-b^2 = -3
b^2 = 3
b = ±3
