Question

1. simplify (9 - 6i)(6 + 3i), writing your answer in terms of i.

(9 - 6i)(6 + 3i) = enter your next step here

Explanation:

Step1: Use FOIL method

$(9 - 6i)(6 + 3i)=9\times6+9\times3i-6i\times6-6i\times3i$
$= 54 + 27i- 36i-18i^{2}$

Step2: Recall $i^{2}=-1$

Since $i^{2}=-1$, we substitute it into the above - expression:
$54 + 27i-36i-18\times(-1)=54 + 18+27i - 36i$

Step3: Combine like - terms

$(54 + 18)+(27i-36i)=72 - 9i$

Answer:

$72 - 9i$