What is the answer 5i / (2+3i) ^2

Simplify the following:5 i / (3 i + 2) ^2

(3 i + 2) ^2 = 4 + 6 i + 6 i - 9 = - 5 + 12 i: (5 i) / 12 i - 5

Multiply numerator and denominator of (5 i) / (12 i - 5) by 5 + 12 i: (5 i (12 i + 5)) / ((12 i - 5) (12 i + 5))

(12 i - 5) (12 i + 5) = - 5*5 - 5*12 i + 12 i*5 + 12 i*12 i = - 25 - 60 i + 60 i - 144 = - 169: (5 i (12 i + 5)) / - 169

i (12 i + 5) = - 12 + 5 i: (5 5 i - 12) / (-169)

Multiply numerator and denominator of (5 (5 i - 12)) / (-169) by - 1:Answer: (-5 (5 i - 12)) / 169