x+y=i
x*y=42
List all possible solutions of the above equation, where i=sqrt(-1).
You need neither pen nor paper.
We are given a sum and product of two variables. Then those variables are the two roots of a quadratic equation. So in effect we want the roots of z^2-iz+42=0.
Pull an i^2 out of 42. Then 42=-42i^2; substitute this in and the quadratic can be treated as a two variable quadratic: z^2-1*iz-42i^2.
So now all we need is the roots to be signed factors of -42 and add to 1. That's easy to find as 7*-6=-42 and 7+-6=1. Then reatttach i to the roots to get the answer x and y are 7i and -6i.
Note: Ady said pencil and paper is not needed, and he is right. My solution in text is just a writeup of the mental thoughts I had to solve the problem.
Solution
