Evaluate this complex number multiplication
(2 + 3i)(9 - 8i)
(a * c) + (b * c) + (a * d) + (b * d)
a = 2, b = 3, c = 9, and d = -8
(2 + 3i)(9 - 8i) = (2 * 9) + (3i * 9) + (2 * -8i) + (3i * -8i)
(2 + 3i)(9 - 8i) = 18 + 27i - 16i - 24i2
(2 + 3i)(9 - 8i) = 18 + (27 - 16)i - 24i2
(2 + 3i)(9 - 8i) = 18 + 11i - 24i2
i2 = √-1 * √-1 = -1, so our last term becomes:
(2 + 3i)(9 - 8i) = 18 + 11i - 24* (-1)
(2 + 3i)(9 - 8i) = 18 + 11i + 24
(2 + 3i)(9 - 8i) = (18 + 24) + 11i
(2 + 3i)(9 - 8i) = 42 + 11i