Imaginary part of complex number (first post)

[bfed]

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)

 

[dx]

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

 

[bfed]

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

and what happens to the A in the function?

 

[dx]

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

 

[bfed]

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]

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.

 

[bfed]

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]

Yep, that's right.

 

[bfed]

good stuff much appreciated dx