Complex Function: Real & Imaginary Parts, Square, Reciprocal & Absolute Value

[UrbanXrisis]

I am to find the imaginary part, real part, square, reciprocal, and absolut value of the complex function:

y(x,t)=ie^{i(kx-\omega t)}
y(x,t)=i\left( cos(kx- \omega t)+ i sin(kx- \omega t) \right)
y(x,t)=icos(kx- \omega t)-sin(kx- \omega t)

the imaginary part is cos(kx- \omega t)

the real part is -sin(kx- \omega t)

the square is:
-cos^2(kx- \omega t)-2icos(kx- \omega t)sin(kx- \omega t)+sin^2(kx- \omega t)
=-cos^2(kx- \omega t)-isin(2kx-2 \omega t)+sin^2(kx- \omega t)
=-\frac{1}{2}(1+cos(2(kx- \omega t))-isin(2((kx- \omega t))+\frac{1}{2}(1-cos(2(kx- \omega t))
=-cos(2(kx- \omega t))-isin(2((kx- \omega t))

the reciprocal is:
\frac{1}{ie^{i(kx- \omega t)}}
=-ie^{-i(kx- \omega t)}
=-icos(kx- \omega t)-sin(kx- \omega t)

absolute value: (not to sure about this...)
=|icos(kx- \omega t)-sin(kx- \omega t)|
cos^2(kx- \omega t)+sin^2(kx- \omega t)
=1?

do these look okay?

 

[quasar987]

We usually talk about the norm of a complex number, not its absolute value.

You're only missing a square root: |x+iy| = \sqrt{x^2+y^2}, but it does not affect the answer.

The rest looks good to me.