Question: How do I get the determinant for a Complex variable Matrix?

I am trying to solve an RLC circuit that uses sinusoidal wave generated voltage supply and I do not understand how to use a complex Matrices. Normally the Matrices of Constant coefflcients is one of a Real Number valued Matrix, but the Phase on the RLC circuit uses a Complex variable, and the elements of the Matrix cannot by combined as real number values because the current in the Mesh Current Method for RLC Sinusoidal Phase Circuit Analysis uses a Vector as the answer for the current...

My Question is How do I set up a Complex Matrix and solve for the determinant?

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