Differentiating complex exponential

[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??

 

[HallsofIvy]

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

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

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??

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

 

[sozener1]

query

Why? The original e^(√3t+1)i why not stay with that? Yes, i is a constant. It's derivative is 0.

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