So [itex]z'(t) = x'(t) + i y'(t)[/itex], I just want to make sure that what I'm going to do is OK. I'm trying to solve [itex]z' = az [/itex] where [itex]a = \alpha + i \beta [/itex](adsbygoogle = window.adsbygoogle || []).push({});

[itex] z'(t) = az(t) \Rightarrow x'(t) + iy'(t) = a(x(t) + iy(t)) \Rightarrow x'(t) = a x(t), y'(t) = a y(t) [/itex]

If you could give me a justification that'll be nice. I feel like what I'm doing is instinctual rather than "I'm following the rules" if that makes any sense.

I mean I've already broken this into the system

[itex] \begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} \alpha & -\beta\\ \beta & \alpha \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} [/itex]

and I know what the general solution looks like here. I'm just trying to compare the two methods. I'm taking an introductory course in Dynamical Systems. Also any suggested books that discusses Solving Differential equations with complex variables will be great.

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# Solving z'(t) = az(t)

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