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...
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...
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...