Thread: How do I solve a system of equations with imaginary parts?

I am doing my differential equations homework and am stuck when I have to solve a system of equations with complex numbers.

For example:

(2-3i)u-5v=0
u+(-2-3i)v=0

I end up getting 0=0. Is there an easy way to do this?

Multiply the second equation by (2 - 3i):

(2 - 3i)u + (-(2 + 3i)(2 - 3i))v = 0 Simplifying,

(2 - 3i)u - 13v = 0
(2 - 3i)u = 13v

Substitute this into the first equation:

13v - 5v = 0
8v = 0
v = 0
u = 13v/(2 - 3i) = 0

So the solution is (0, 0)