Answer :
To simplify something like that, you just multiply numerator and denominator by conjugate of denominator.
Our denominator is 5-8i, so our conjugate of denominator would be 5+8i.
[ (-3-9i)(5+8i) ] / [ (5-8i)(5+8i) ]
Now we can simplify from here;
[ -15 - 45i - 24i - 72i^2 ] / [ 25 - 64i^2 ]
[ -15 - 45i - 24i + 72 ] / [ 25 + 64 ]
[ 57 - 69i ] / [ 89 ]
Answer: (57 - 69i) / 89
Hope this helps.
Our denominator is 5-8i, so our conjugate of denominator would be 5+8i.
[ (-3-9i)(5+8i) ] / [ (5-8i)(5+8i) ]
Now we can simplify from here;
[ -15 - 45i - 24i - 72i^2 ] / [ 25 - 64i^2 ]
[ -15 - 45i - 24i + 72 ] / [ 25 + 64 ]
[ 57 - 69i ] / [ 89 ]
Answer: (57 - 69i) / 89
Hope this helps.
