Question

Simplify (3 + 2i)(7 − 5i).

Answer 1

(3+2i)(7-5i) = 21 - 15i + 14i + 10 = 31 - i

Answer 2

Rule needed: i^2 = -1
Standard form a + bi

(3 + 2i)(7 - 5i) FOIL
3 * 7 = 21
3 * - 5i = - 15i
2i * 7 = 14i
2i * -5i = - 10i^2 = - 10 * -1 = 10
Putting it all back together.
31 - i