Holomorphic function

Let f(z) be holomorphic in |z|less than R with Taylor expansion f(z)=sum(a_nz^n) and set I_2(r)=1/2pi(integral from 0 to 2pi of|f(re^itheta)|^2 d(theta), where 0<=r

Poisson kernel

Let P_r(t)=R((1+z)/(1-z)), z=re^it be the Poisson kernel for the unit disc |z|<1. Let U(theta) be a continous function of the interval [0,pi] with U(0)=U(pi)=0. Show that the function u(re^itheta)=1/2pi(integral from 0 to pi of {P_r(t-theta)-P_r(t+theta)}U(t)dt is harmonic in the half-disc {re^itheta,0<=r<1, 0<=theta<=pi} and ...continues

if y = xsinx prove that...

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Solving equations

I need to solve for all of the roots of (z+1)^4 = (1-i). Any idea on how to do it?

Solving complex variable equations

Find the values of: i^(Sqrt(3)) The answer is: cos(pi*sqrt(3)[1/2+2k]) + i.sin(pi*sqrt(3)[1/2+2k]), for any integer k.

Solve the following equation for z

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Prove the following using only the information given

Prove that sin2 x + cos2 x = 1 using only this information. See attached file for full problem description.

Complex Variables

Any insight on where to go with these problems would be helpful and appreciative. This is my first time in complex analysis and I am having problems understanding the concepts. Seeing solutions to problems is helping me to understand how to approach other problems. See attached file for full problem description.

Complex variables II

Any insight on where to go with these problems would be helpful and appreciative. This is my first time in complex analysis and I am having problems understanding the concepts. Seeing solutions to problems is helping me to understand how to approach other problems. Thank you very much! I need help specifically on problems ...continues

Complex Variables

Complex Variables. See attached file for full problem description.