Recent content by Mark C

Advanced math is not "boring mechanical calclation" it is about about proofs. Thats where the "non-mechanical" stuff kicks in. In advanced math classes, no one "counts" or integrates anything.

I am not supposed to use the formula for arctan w.

Well, yes I know that, I can show that if w=i or -i then the expression is not defined, but that's not the same thing. thank you anyway

Hi If w=tan z How would I show that any w not equal to +i or -i, is the image of some z in C, and what are the solutions of w=tan z if w doesn't equal to +i or -i? I can easily show that tan z can never equal +i or -i, but that's not the same thing also. Note: without using the...

If I show, that w = 4(pi)n works for all z (n an integer), then I do not find all such w that do this, for all z in C, because 2(pi), works also, but is not in the set 4(pi)n , n an integer. So, if I would claim that all w=4(pi)n works for all z, this is true, but, I do not find all such w.

Yes, w=2(pi) is certainly one solution, and showing that w = 2(pi)n (n an integer), works for all z is easy. However, how could I know that there are no other w that do this? Meaning, I could also show w = 4(pi)n works for all z, but those are not all the w's possible. Thanks

Hi, How would I do the following: Find all w in C, such that cos(z + w) = cos z, for all z in C. Of course I would need to use the identity cos z = (e^iz +e^-iz)/2, but I have trouble finding w for all z. Thank you