The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 22 i Which statement must be true about the complex numbers?
Answer
A
The complex numbers have equal imaginary coefficients.
B
The complex numbers have opposite imaginary coefficients.
C
The complex numbers have opposite real numbers.
D
The complex numbers have equal real numbers.
Explanation
Write the complex numbers as a + bi and c + di. Their sum is (a + c) + (b + d)i; for this to equal 22i, its real part must be 0, so a + c = 0. Therefore, the numbers have opposite real parts, as stated in choice C.
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