How do I simplify complex numbers and find real and imaginary parts?

[danik_ejik]

Hello,
I need to simplify and find Re and I am of

.

I've multiplied by

and got that Re=

and Im=

.

Is that the correct way and a correct result ?

 

[sachinism]

seems fair to me

 

[ehild]

Show your work in detail. The final result is wrong. How did you get cos x in the denominator?

ehild

 

[danik_ejik]

here's my work in details,
http://img811.imageshack.us/img811/7444/exsol.jpg"

 

[ehild]

It is better if you type in your work.

I found a typo: You wrote that e^-ix=cos (2x)-isin(2x).

ehild

 

[danik_ejik]

it should have been
[URL]http://latex.codecogs.com/gif.latex?e^{-i2x}[/URL]
so the latter expansion is correct.

 

[ehild]

OK, I see now. But you should exclude x=(2k+1)pi/2 before multiplying both numerator and denominator by 1+exp(-2ix) which is 0 if x=(2k+1)pi/2.

 

[danik_ejik]

oh, forgot about that.
thanks

 

[ehild]

It would have been simpler to factor out exp(ix) from the denominator:

$$\frac{1+e^{ix}}{1+e^{2ix}}=\frac{1+e^{ix}}{e^{ix}(e^{-ix}+e^{ix})}=\frac{e^{-ix}(1+e^{ix})}{2\cos{x}}$$

ehild