The question:
Show that for any complex number z with |z| = 1.
My attempt:
I tried finding the the result of the division, hoping to get a value of 0 as the real part, to confirm the problem. This is what I got:
Let z = a+ib
Therefore the real part is:
Now I'm not sure where to go from here. I think what I've done so far is correct. Any help would be great, thanks!
I think you have a mistake either in your calculation or your writing. the final expression is:
[LaTeX ERROR: Convert failed]
Now, since the magnitude of z is 1, you have [LaTeX ERROR: Convert failed] . Thus the numerator simplifies to 0 and hence the statement is proven!
Edit: Didn't see you post Archie Meade.
Looks like an error here, perhaps a typo. " " in the denominator of the first fraction has become " ". Also " " in the denominator has become " " but since a fraction is 0 if and only if the numerator is 0, the denominator is irrelevant.
The numerator shoud be - and .
Therefore the real part is:
Now I'm not sure where to go from here. I think what I've done so far is correct. Any help would be great, thanks!