and so that
where and .
when solving a system of differential equations of the form
dy/dt = Ay
The constant vector lambda is found with
|A - lambda * I| = 0
If lambda is a complex number I have the solution to
A = [4, -2; 5, 2]
with lambda = 3 + 3i
y = A Re {[2; 1-3i]exp(3+3i)t} + B Im {[2; 1-3i]exp(3+3i)t} (1)
= A exp(3t)[2cos3t; cos3t + 3sin3t] + B exp(3t)[2sin3t; sin3t - 3cos3t] (2)
The question, how do i get from equation (1) to (2)???
does the imaginary part equal sin and the real part equal cos??