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