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## Homework Statement

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

## Homework Equations

## The Attempt at a Solution

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

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- Thread starter bfed
- Start date

In summary, to find the imaginary part of the function C = A*e^(-i*wt)*sin(k*x), use Euler's formula eiθ = cos(θ) + i sin(θ) to expand the expression and then simplify it. The coefficient of i will be the imaginary part of C. After substituting the expanded expression back into the original, use the distributive law of multiplication to expand the brackets. The resulting expression will be of the form C = R + iI, where I is the imaginary part of C.

- #1

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

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

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- #2

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- #3

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

and what happens to the A in the function?

and what happens to the A in the function?

- #4

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No, that's not right. What is the expression you got after using Euler's formula to expand C?

- #5

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then do i substitute it back into the original expression?

- #6

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

- #7

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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

- #8

Homework Helper

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Yep, that's right.

- #9

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good stuff much appreciated dx

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