Derivative on Complex Number (1 Viewer)

[addikaye03]

Just checking if my answer is correct:

Q. Use complex exponential to find the 9th derivative of sint/(e^rt3t). Simpliest form

S. Im(e^it).e^-rt3t

Im{d^9/dt^9[e^(i-rt3)t]}

Im[(i-rt3)^9e^-rt3t cos(t)+i(i-rt3)^9e^-rt3.sint]

Im[2^9e^i(45pi/6)e^-rt3cost +i(2^9e^i(45pi/6)(e^-rt3)(sint)]

=[(512e^i45pi/6)sint]/(e^rt3)

=[(512(0)+i512sin(-90)]sint/(e^rt3)

=(-512i)sint/(e^rt3)

Is this correct? can i add anything? Is there an alternative method so that i can check my answer after i've used the above method?

Thanks

 

[shaon0]

Just checking if my answer is correct:

Q. Use complex exponential to find the 9th derivative of sint/(e^rt3t). Simpliest form

S. Im(e^it).e^-rt3t

Im{d^9/dt^9[e^(i-rt3)t]}

Im[(i-rt3)^9e^-rt3t cos(t)+i(i-rt3)^9e^-rt3.sint]

Im[2^9e^i(45pi/6)e^-rt3cost +i(2^9e^i(45pi/6)(e^-rt3)(sint)]

=[(512e^i45pi/6)sint]/(e^rt3)

=[(512(0)+i512sin(-90)]sint/(e^rt3)

=(-512i)sint/(e^rt3)

Is this correct? can i add anything? Is there an alternative method so that i can check my answer after i've used the above method?

Thanks

-512cos(t).e^-sqrt(3)t is the answer i got. But idk if its right because i haven't done anything like this before, might post up a solution later.

 

[addikaye03]

-512sin(t)e^-sqrt(3)t I believe ( the 'i' wasn't supposed to be in it). It's definitely sin(t) not cos(t) since it's the Imaginary component of the derivative, cos(t) is the real.

 

[untouchablecuz]

this is what i get

 

[livvy-love]

I am having a problem with this question also - addikaye03, I have done exactly what you have done and ended up with (-512)sint/(e^rt3)

Yet, the calculator says the answer is (-512)cost/(e^rt3), and pretty sure when you actually do the derivative thing 9 times you would end up with cos.
WHYYYY?!

 

[untouchablecuz]

I am having a problem with this question also - addikaye03, I have done exactly what you have done and ended up with (-512)sint/(e^rt3)

Yet, the calculator says the answer is (-512)cost/(e^rt3), and pretty sure when you actually do the derivative thing 9 times you would end up with cos.
WHYYYY?!

in my previous answer i made the mistake of not multiplying i(5pi/6) by 9. this amended answer gives the correct solution: