The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 34i. Which statement must be true about the complex numbers?

Write the complex numbers as a + bi and c + di. Their sum is (a + c) + (b + d)i, and since it equals 34i, its real part is zero, so a + c = 0. Therefore a = −c: the numbers have opposite real parts. The condition that their real parts are nonzero means neither part is zero, but it does not require the imaginary parts to match.

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