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Answer

↓Steps Explained:↓

Evaluate this complex number multiplication

(9 - 6i)(2 - 4i)

Define the FOIL Formula:

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

Set the FOIL values:

a = 9, b = -6, c = 2, and d = -4

Plug in values:

(9 - 6i)(2 - 4i) = (9 * 2) + (-6i * 2) + (9 * -4i) + (-6i * -4i)

(9 - 6i)(2 - 4i) = 18 - 12i - 36i + 24i²

Group the like terms:

(9 - 6i)(2 - 4i) = 18 + (-12 - 36)i + 24i²

(9 - 6i)(2 - 4i) = 18 - 48i + 24i²

Simplify our last term:

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

(9 - 6i)(2 - 4i) = 18 - 48i + 24* (-1)

(9 - 6i)(2 - 4i) = 18 - 48i - 24

Group the 2 constants

(9 - 6i)(2 - 4i) = (18 - 24) - 48i

Final Answer