1. ## Complex exponential function

|1-e-i2pi x+0.5e-i4pix|2

Can someone help me develop this to find the correct answer?
Thank you

2. ## Re: Complex exponential function

Originally Posted by mathfn
|1-e-i2pi x+0.5e-i4pix|2
Can someone help me develop this to find the correct answer?
Do you know that $\overline{\exp(i\theta)}=\exp(-i\theta)$ You should prove it (hint: odd & even functions)
Also use the fact that $|z|^2=z\cdot\overline{z}$

So all you must do is multiply $(1-\exp(-i 2\pi x)+0.5\exp(- 4 i\pi x))(1-\exp(i 2\pi x)+0.5\exp(4 i\pi x))$

3. ## Re: Complex exponential function

Thank you so much, very helpful