Complex number problem

If i = √-1, which of the following expressions shows the square of the sum (2i + 3) + (2 – 6i)?

A. 41 + 40i

B. 9 + 40i

C. 41 – 40i

D. 9 – 40i

You may be tempted to square the sum right away, but it is simpler to add the numbers before squaring them. The sum is 2 + 3 – 6i + 2i = 5 – 4i. Squaring this result produces 5 • 5 + 2 • 5 • (-4i) + (-4i) • (-4i) = 25 – 40i + 16i² = 25 – 40i + 16(-1) = 25 – 16 – 40i = 9 – 40i. Thus the correct choice is (D).

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