General Solution for a 2x2 Matrix with Complex Eigenvalues

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The discussion focuses on finding the general solution for the system defined by the matrix x'=(3, 4, -2, -1)x, which has complex eigenvalues 1+2i and 1-2i. The user initially seeks to express the solution in terms of real-valued functions and identifies the eigenvalues and corresponding eigenvectors. After some deliberation, the user concludes they have found the solution. The conversation highlights the process of working with complex eigenvalues in a 2x2 matrix context. Ultimately, the user successfully arrives at the answer without further assistance.
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Express the general solution of x'=(3, 4, -2, -1)x in terms of real-valued functions.

This is 2x2 matrix, 3 and 4 on the left, -2 and -1 on the right. I know that the eigenvalues are 1+2i, 1-2i. And a=1, b=1+i for the first eigenvalue. a=1, b=1-i for the second eigenvalue. But how do I get the answer?
 
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Never mind. I got it.
 

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