Which values of p and q would make the value of the following expression equal to 58 i ? open paren 3 minus 7 i close paren times open paren p plus q i close paren times i

First multiply the last factor: (3 − 7i)i = 7 + 3i. Then (7 + 3i)(p + qi) has real part 7p − 3q and imaginary part 7q + 3p. For the result to equal 58i, the real part must be 0 and the imaginary part must be 58. With p = 3 and q = 7, these are 21 − 21 = 0 and 49 + 9 = 58, so the correct choice is D, p = 3 and q = 7.

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