Sum of complex radicals squared

Question

I am solving an exercise of complex numbers. The problem is that my result was -12 and the correct result is 12i.

Exercise:

My development:

Could you tell me what I'm failing?

Answer 1

What you've stumbled upon is the common error called Freshman's Dream. The core problem is that's not how you square quantities. $(a-b)^2$ is $a^2-2ab+b^2$, not $(a^2-b^2)$.

That said, the answer is not $12i$ because there are both real and imaginary terms once you square the quantity, since you do not have a difference of squares.