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? a. the complex numbers have equal imaginary coefficients. b. the complex numbers have equal real numbers. c. the complex numbers have opposite imaginary coefficients. d. the complex numbers have opposite real numbers.

 The correct option is

(D) The complex numbers have opposite real numbers.

Step-by-step explanation:  Given that the sum of two complex numbers with non zero real parts is 34i.

We are to elect the TRUE statement about the complex numbers.

Let z = a + bi  and   z' = a' + b'i be the given complex numbers.

Then, according to the given information, we have

Equating the real and imaginary parts from both sides of the above equation, we get

Therefore, the real parts of both the complex numbers are opposite to each other.

Thus, (D) is the correct option.

step-by-step explanation: