The square of any complex number is

a^2 - b^2 + 2abi

Step-by-step explanation:

Let a = a + bi

Then, z^2 = (a + bi) ^2

= a^2 + 2abi + (bi) ^2

= a^2 + 2abi + (b^2) (i^2)

Since i^2 = - 1,

z^2 = a^2 + 2abi - b^2

z^2 = a^2 - b^2 + 2abi

raised to the second power: ^2