Derivative using complex exponential

[forty]

I'm trying find the 15th derivative of exp[(1 + i(3^.5))theta] with respect to theta

To do this do i need to split it into two exponentials, (e^theta).(e^i(3^.5)theta) ??

 

[HallsofIvy]

What is the derivative of e^ax with respect to x? What is its second derivative? What is its 15th derivative? Do you see my point?

 

[forty]

[(1+i(3^.5))^15].e^[(1+i(3^.5))theta]

So i can just apply the normal rules for exponentials ??

 

[HallsofIvy]

Yes, 1+i(3^.5) is "just a number". You might want to use De Moivre's formula to caculate $(1+ i\sqrt{3})^{15}$ itself.