Recent content by de1irious

If p(z)=a0+a1z+...+anz^n, and max|p(z)|=M for |z|=1, show that each coefficient ak is bounded by M. I'm trying to take derivatives but it's not getting anywhere. Thanks!

Hi, so suppose f(z) is a complex function analytic on {z|1<|z|} (outside the unit circle). Also, we know that limit as z-->infinity of zf(z) = A. Now I need to show that for any circle C_{R} centered at origin with radius R>1 and counterclockwise orientation, that \oint f(z)dz = 2\pi iA...

Haha :rolleyes: Actually I think I figured it out. You can show two-moves contain a certain other kind of move, which more clearly is able to separate components of a link.

Hi, so I need to show that every link is two-equivalent to a trivial link with the same number of components. Right now I can show that if I have a simple link with linking number = 1, then it is possible to immediately separate the link into its two components. But how can I generalize this...

Nvm, I just realized you were talking about hyperbolic sines. Thanks for the tip! EDIT: However, now I get e^{50z}\frac{sinh101z/2}{sinhz/2} Any way to simplify the exponent out front?

I don't think that works though because sin(z) puts the exponent of e as iz and -iz, not z. For instance, if I plug that into a calculator, it doesn't come out equal. I am trying to factor out the real part, but the ratio will not cancel to the point that I have just sines.

That's fine, Mathman. If we allow sin to be evaluated at complex numbers, using the standard definition of sin(z) in terms of the exponential, how do we we rewrite it? Thanks

Is it possible for me to write this complex fraction as a ratio of two sines? Thanks. \frac{1-e^{101z}}{1-e^{z}}

I need to show that the coefficients of a complex polynomial P(z) are real iff P(x) is real for all real x. Thanks!

Hi, I am just wondering if the zero product property (ab=0 implies a=0 or b=0) can be proven on the integers, or is it directly axiomatic to the defining of the integers? Also, where might I find a definition of the integer axioms? Thanks a lot,

nvm this is easy. thanks for the help

For small x, it seems sqrt(1+x) can be approximated by 1+x/2. Why exactly is this? Is there a theorem that I can refer to? Some kind of infinite series where the x^4 power term dies out? Thanks!

How do you show that the exponential function is its own derivative by using the fact that E(x)E(y)=E(x+y). Don't assume the derivative exists either. You can use any other property of E(x) that you can think of, but you are supposed to use the fact above primarily. (that is, without using the...

You mean this limit comparison test? http://mathworld.wolfram.com/LimitComparisonTest.html But what limit does it tend to? I thought |cos n| didn't tend to a limit as n--> infinity.

Hi sorry, I'm having trouble understanding that. How am I supposed to compare that?