Need help with a complex inequality??
hey!
i been trying to do this inequality for a 2 hrs now and can't seem to prove it
|\frac{1}{2}(a+b)|^p \leq \frac{1}{2}(|a|^p+|b|^p) where a,b are complex numbers
Can anyone suggest a way??
thanks
I figured that we have to use complex numbers but we weren't told a method how to factorise complex polynomials with say n degree.Can you tell me a method of how to factorize a complex polynomial??
You mentioned that the quote above is the theorema egregium of Algebra which I am having...
Do you know the name of it because of never heard of it.I wouldn't know where to start.If i have the name i can probably do some research on it and continue from there maybe
I don't see where you going.The roots you can get from the product..do want me to replace z with \cos\theta+i\sin\theta
hmmm...with the
LHS = (\cos\theta+i\sin\theta)^{n+1}-1=(\cos(n+1)\theta+i\sin(n+1)\theta)-1
and RHS =...
sorry!yes i was missing something in the original equation.So it suppose to look like this
(z^(n+1))-1 = Product[(z-exp[2*Pi*i*(j+1)/(n+1)]) , 0<=j<=n]
where
Product[(z-exp[2*Pi*i*(j+1)/(n+1)]) , 0<=j<=n] = (z-exp[2*Pi*i*(0+1)/(n+1)]*(z-exp[2*Pi*i*(1+1)/(n+1)]*...*(z-exp[2*Pi*i*(n+1)/(n+1)]...
Hey!I have a tut question and I am having problems proving
(z^(n+1))-1 = (z-exp[2*Pi*i*(j+1)/(n+1)]) where 0<=j<=n
I tried doing it by induction which is easy for the 1st case with n = 1,I assume the case n-1 but then i get stuck with the last case.
How will i know that all the z's with...