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??