Complex numbers, multiplying by the conjugate. Book differs to my answer.?

Question

I was presented the question: (12 - 8j) / ((2 + j)^2). I got the answer (4 - 72j) / 25. The book however says it;s (-1 -3/2 j).

Who's correct?

Answer 1

You are correct.
(2+j)² = 4-1 + 4j = 3+4j
Now multiply top and bottom of your fraction by 3-4j to get
(12-8j)(3-4j)/25
= (4-72j)/25.
Probably the author of the book changed the
problem in a subsequent edition but forgot to change
the answer in the back of the book.

Answer 2

N = 12 - 8 j
D = ( 2 + j ) ( 2 + j ) = 4 + 4 j + j ² = 3 + 4 j
N / D = (12 - 8 j ) / ( 3 + 4 j )
N / D = ( 12 - 8 j ) ( 3 - 4 j ) / 25
N / D = ( 36 - 72 j - 32 ) / 25
N / D = ( 4 - 72 j ) / 25
N / D = ( 4 / 25) ( 1 - 18 j )

Answer 3

I get the same answer as yours. Maybe it's an error in the book. It happens.