Question

What is the value of the product (3 – 2i)(3 + 2i)?

A. 5
B. 9 + 4i
C. 9 – 4i
D. 13

Answer 1

D. 13

Explanation:

(3 – 2i)(3 + 2i)

= 9 + 6i - 6i - 4i^2

= 9 - 4i^2

Since i = √-1, i^2 = -1

9 - 4i^2 = 9 - 4(-1) = 9 + 5 = 13

Answer 2

D. 13

Explanation:

You can do the product in the straight-forward way ...

... (3 -2i)(3 +2i) = 3·3 +3·2i -3i·3 -(2i)(2i)

... = 9 +6i -6i -4i² . . . . . note the middle two terms cancel

Recognize that i = √-1, so i² = -1. Then the sum is

... = 9 -4(-1) = 9+4 = 13

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Your graphing calculator can do this product, too.