Recent content by nickolas2730

am i doing this prove by liouville's theorem? can i do it like this: suppose f = 1/e^f(z)=1/e^ Im(f) < 1/e^M so it is bounded by liouville's theorem, it is constant

1. Evaluate ∫C (z)/z2+9 dz , where C is the circle │z-2i│=4. what i have done so far is : z(t) = 2i + 4eit z'(t) = 4ieit f(z(t)) = 4ieit/(4ieit)2+9 ∫ (4ieit/(4ieit)2+9) (4ieit) dt intergrate from 0->2pi but i don't know how to solve this intergral, can anyone help? 2. ∫c...

thanks!

Q:Let f be entire and suppose that I am f(z) ≥ M for all z. Prove that f must be a constant function. A: i suppose M is a constant. So I am f(z) is a constant which means the function is a constant. Am i doing this right ? but i don't think there will be such a stupid question in my...

so if C is the circle of │z - 2i │= 4 z(t) = 2i + 4e^it ? i am doing it right?

compute the integral ∫Cr (z - z0)n dz, with an integer and Cr the circle │z - z0│= r traversed once in the counterclockwise direction Solution: A suitable parametrization for Cr is give by z(t)= z0 + reit 0≤t≤2π ... ... My question is , how to find that suitable z(t)? i have no idea...

thanks, i know eπi=-1 but the problem is , when i was in exam i was looking at the -1 , how can i know e?, what about the question is -2 , do i need to try it one by one like π/2,π/3...

i know there is an equation : ez1=ez2 holds if and only if z1=z2 + 2kπi But how can i know in exam -1 = eπi is it by try an error

Prove that cos z = 0 if and only if z = π/2 + kπ, where k is an integer. The solution is : cos z = (eiz+e-iz)/2 = 0 <=>eiz+e-iz)=0 <=>e2iz=-1 <=>2iz=πi +2kπi <=>z=π/2 + kπ But i don't understand how does these 2 steps work <=>e2iz=-1 <=>2iz=πi +2kπi how can a exp function...

thank you again =]

oh i see, which means the ans for log and arg must comtain something like 2kπ, which makes them as a set of solution?

In my complex analysis textbook, there is a definition about log function, which is: log z := Log |z| + i arg z = Log |z| + i Arg z + 2kπ where k = 0,±1,±2... my question is , is there any different between log and Log, and arg and Arg? If yes, what's the different between them

P ((1 −√3i)1−i) = e(1−i)Log(1−√3i) = e(1−i)(ln 2− ∏/3 i) = eln 2−∏/3 e−(ln 2+∏/3)i

sure! btw, thanks for helping me for the homework question b4

Thank you so much, i have handed it in already lol and waiting for answer and see what on Earth does that P stand for