Solution strategy for x'=Ax if A has complex eigenvalues

How can we solve x'=Ax if A has complex eigenvalues? We will do this in the two by two case. In this case we know that A is similar to a scaling rotation matrix C.
In a linear algebra course you may have learnt how to do this. In this video we will review the steps. These steps will give us a complicated final expression for two independent solutions.

How can we memorize this solution? We will also show a trick to memorize and compute the two solutions easily. And similar to the diagonalizable case,
we recommend to memorize this final expression.

From now we will often use it, without doing all the Linear Algebra steps inbetween anymore, because this will allow us to do our computations a bit faster and more smoothly.