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?

Answer 1

Call these complex numbers \(z_1\) and \(z_2\). You have
\[\text{Re}(z_1+z_2)=0\]
which means you must have
\[\text{Re}(z_1)+\text{Re}(z_2)=0~~\iff~~\text{Re}(z_1)=-\text{Re}(z_2)\]
This looks like a multiple choice question, so there's a chance this is an option. No telling unless you list the answer choices.