Please note that is pronounced "theta" and that you have got the wrong sign in the above formula. It should be .

This formula is valid if, . To see this you need to know that

(1) , by definition of

and (2) that .

Thus, overall you get that

what was to be shown.

Similarly for

If you know that , it is easy to see that if , it follows that .and

sin(pheta= 1/2i(z-1/z)

are given formulas? (if anyone knows?)

and finally I do not understand how to get from the step where I worked out all z's in my brackets to an answer that makes sense.

Thus,

Where the equivalence that I have marked red follows from the above formula , if you subtitute for and for .