Differentiating complex numbers?

[Shaybay92]

I am not sure whether there is any difference between differentiating complex and real numbers... I am just trying to differentiate:

e^(2+3i)x = (2+3i)e^(2+3i)x

Is this correct? I have a feeling its not this simple.

 

[Pengwuino]

No that's fine. It's good that wanting to do that gives you pause, but if you grab any introductory complex analysis text, you'll find simple things like this are fine. There are situations where differentiation is not so simple, but the only ones i can remember are when you're trying to differentiate awkward functions such as f(z) = |z|^2 where z is a complex number. In that case the derivative works only at z=0 or something of that sorts.