The additive inverse of a number is that number when added to the first has a sum of zero. We know that zero is defined in the complex numbers by . So the task is to find such that
We know that the sum of two complex numbers is found by adding the real part coefficients and by adding the imaginary part coefficients.
Hence, the task is reduced to solving the following two equations:
And
for and and then substituting those values back into the original complex variable .
Completion of the task is left as an exercise for the student. When you are done, an easier way to do this should suggest itself. What is that easier way?
