# Differentiating complex exponential

1. Sep 3, 2014

### sozener1

I asked to differentiate the given function using exponential function

with sin(√3t + 1) I turned it into Im[e^(√3t+1)i]

then I multiplied it by e^t

which gave Im[e^t*e^(√3t +1)i]

then I applied usual algebra to differentiate but I get a (t+√3ti +i) as the power of e

when I try to differentiate (t+√3ti +i) with respect to t I can do it with the first two terms but not i

how do you do differentiation over i? does it go to zero??

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2. Sep 3, 2014

### HallsofIvy

Staff Emeritus
Why? The original e^(√3t+1)i why not stay with that?

Yes, i is a constant. It's derivative is 0.

3. Sep 4, 2014

### sozener1

query

Just for assurance would you be able to get the derivative of order 8

with just e^(√3t+1)i ??

Cos the original function given was e^t*e^(√3t+1)i

as it was uploaded as an image file