# Imaginary part of complex number (first post)

## Homework Statement

C=A*e^(-i*wt)*sin(k*x); A,w,t,k,x are real numbers. Find imaginary part.

## The Attempt at a Solution

Im(C)=cos(wt)-i*sin(wt)

## The Attempt at a Solution

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dx
Homework Helper
Gold Member
Use Euler's formula e = cos(θ) + i sin(θ), and then simplify the resulting expression. The coefficient of i will be the imaginary part of C.

so then the imaginary party would be sin(wt)?

and what happens to the A in the function?

dx
Homework Helper
Gold Member
No, thats not right. What is the expression you got after using Euler's formula to expand C?

e^(-iwt)=cos(wt)-i*sin(wt) is how I think to the Euler formula...

then do i substitute it back into the original expression?

dx
Homework Helper
Gold Member
Yes, substitue it back into the original expression, and then expand out the brackets using the distributive law of multiplication, i.e. A(B + C) = AB + AC.

Then you will have an expression of the form C = R + iI, and I is the imaginary part of C.

so...

C=A*cos(wt)*sin(kx)-i*A*sin(wt)*sin(kx)

Re(C)=A*cos(wt)*sin(kx)
and
Im(C)=-A*sin(wt)*sin(kx)

is this the proper solution?

And thanks dx

dx
Homework Helper
Gold Member
Yep, thats right.

good stuff much appreciated dx