Help with My complex functions

[json078]

Help with My complex functions :(

Homework Statement

I have to find a real part and Imaginary part of complex functions
but I kinda stuck on this question :(

Homework Equations

f(t)=e(-1+2i)(2-i ; 3+4i)

from this equation I have to find real part and imaginary part :(
I need ur help guyz asap
!:) cheers

The Attempt at a Solution

 

[Mark44]

Homework Statement

I have to find a real part and Imaginary part of complex functions
but I kinda stuck on this question :(

Homework Equations

f(t)=e(-1+2i)(2-i ; 3+4i)

from this equation I have to find real part and imaginary part :(
I need ur help guyz asap
!:) cheers

The Attempt at a Solution

There seems to be something missing in your function. The expression on the right side doesn't have t in it. Is this the formula for your function?
f(t) = e^{(-1 + 2i)t}(2 - i; 3 + 4i)

 

[json078]

true that
the original function is
f(t) = e(-1+2i)t[2-i ; 3+4i]

 

[HallsofIvy]

What you have written makes no sense. What is that "e" doing in your formula? Do you really mean it to just be multiplied or do you intend e^{(-1+ 2i)t}? And what is "[2-i ; 3+4i]" is this a "vector valued" function? And, if so, do you want the real and imaginary parts of each component?

 

[Mark44]

Your vector-valued function can be written this way:
f(t) = <(2 - i) ^{e(-1 + 2i)t} , (3 + 4i)^{e(-1 + 2i)t}>

Then split up the exponentail parts using the fact that e^{(a + b)t} = e^ate^bt. Use the fact that e^ix = cosx + isinx. These should get you started.

 

[Char. Limit]

Your vector-valued function can be written this way:
f(t) = <(2 - i) e^{(-1 + 2i)t} , (3 + 4i)e^{(-1 + 2i)t}>

Then split up the exponentail parts using the fact that e^{(a + b)t} = e^ate^bt. Use the fact that e^ix = cosx + isinx. These should get you started.

Just moved the "e"s outside of the superscript for you.

 

[Mark44]

Thanks. I hadn't noticed they were superscripts also.