If $$(3i-2)^2+(5i+6)^2=a+ib$$​, what is the value of $$a+b$$​?

Correct option is C

​$$\begin{aligned}&\text{Expand } (3i - 2)^2 \\&(3i - 2)^2 = (3i)^2 - 2 \cdot 3i \cdot 2 + 4 = -9 - 12i + 4 = -5 - 12i \\[10pt]&\text{Expand } (5i + 6)^2 \\&(5i + 6)^2 = (5i)^2 + 2 \cdot 5i \cdot 6 + 36 = -25 + 60i + 36 = 11 + 60i \\[10pt]&\text{Add both results} \\&(-5 - 12i) + (11 + 60i) = (-5 + 11) + (-12i + 60i) = 6 + 48i \\[5pt]&\text{So:} \quad a + ib = 6 + 48i \\[10pt]&\text{Find } a + b \\&a = 6, \quad b = 48 \Rightarrow a + b = 6 + 48 = {54}\end{aligned}$$​​