The most reliable way to evaluate this is to eliminate the complex number from the denominator first:
15 + 8i 3 + 4i 45 + 24i + 60i - 32 13 + 84i
z = ------------ * ----------- = ----------------------------- = ----------------
3 - 4i 3 + 4i 9+16 25
Just find the magnitude (abs. val.) of 13 + 84i and then divide the result by 25.
