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Evaluate the expression (4 - 4i)(5 - 9i) and write the result in the form a + bi. The product is ____

Evaluate the expression (4 - 4i)(5 - 9i) and write the result in the form a + bi. The product is ____

Answer

First, expand the expression using the distributive property (FOIL method):

(4)(5) = 20
(4)(-9i) = -36i
(-4i)(5) = -20i
(-4i)(-9i) = 36i²

Since i² = -1, we have:

36i² = 36(-1) = -36

Combine the real and imaginary parts:

Real part: 20 - 36 = -16
Imaginary part: -36i - 20i = -56i

Thus, the result is: -16 - 56i

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