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Answer

↓Steps Explained:↓

Evaluate this complex number multiplication

(2 + 3i)(9 - 8i)

Define the FOIL Formula:

(a * c) + (b * c) + (a * d) + (b * d)

Set the FOIL values:

a = 2, b = 3, c = 9, and d = -8

Plug in values:

(2 + 3i)(9 - 8i) = (2 * 9) + (3i * 9) + (2 * -8i) + (3i * -8i)

(2 + 3i)(9 - 8i) = 18 + 27i - 16i - 24i²

Group the like terms:

(2 + 3i)(9 - 8i) = 18 + (27 - 16)i - 24i²

(2 + 3i)(9 - 8i) = 18 + 11i - 24i²

Simplify our last term:

i² = √-1 * √-1 = -1, so our last term becomes:

(2 + 3i)(9 - 8i) = 18 + 11i - 24* (-1)

(2 + 3i)(9 - 8i) = 18 + 11i + 24

Group the 2 constants

(2 + 3i)(9 - 8i) = (18 + 24) + 11i

Final Answer