Question

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?
The complex numbers have equal imaginary parts.
The complex numbers have equal real parts.
The complex numbers have opposite imaginary parts.
The complex numbers have opposite real parts.

Answer 1

Let the numbers be a + bi and c + di. Their sum is (a + c) + (b + d)i = 0 + 34i, so a + c = 0 and b + d = 34. Since a and c are nonzero but add to zero, c = −a. Thus the real parts are opposites.