Which values of p and q would make the value of the following expression equal to 58i? (3 – 7i)(p + qi)i

First, multiply the last factor by i: (p + qi)i = -q + pi. Then (3 − 7i)(−q + pi) has real part −3q + 7p and imaginary part 3p + 7q. For p = 3 and q = 7, the real part is 0 and the imaginary part is 58, so the expression equals 58i; the correct choice is p = 3, q = 7.

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