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  1. B

    Estimating complex integral

    Homework Statement I need to establish the estimate and inequality |\int_{C} e^{iz^{2}}dz| \leq\frac{\pi(1-e^{-R^{2}}}{4R} < \frac {\pi}{4R} where C={z(t)=Re^{it},t\in[0,\fraq{\pi}{4}] Homework Equations The Attempt at a Solution I thought perhaps I could use the ML equality but...
  2. B

    Complex analysis problem

    Homework Statement Consider the equation (z-1)^23 = z^23 Show that all solutions lie on the line Re(z)=1/2 How many solutions are there Homework Equations The Attempt at a Solution Really have no idea. I figured polar form might be helpful somehow so I converted it and got...
  3. B

    Fixed point iteration to find the roots of 0=x-tan(x)

    Homework Statement The question wants me to first estimate the roots by drawing the graph and then by using a 'suitable' fixed point method to determine the first 4 positive roots. Homework Equations 0=x-tan (x) I rearranged to get x=arctan (x) so that the series x_n will converge...