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**Homework Statement**

Integrate [itex]e^{iz^2}[/itex] around the contour C to obtain the Fresnel integrals:

[tex]\int_0^\infty \cos(x^2) \, dx = \int_0^\infty \sin(x^2) \, dx = \frac{\sqrt{2\pi}}{4}[/tex]

The contour consists of three parts:

- z = x, [itex]0 \le x \le R[/itex]
- z = [itex]Re^{i\theta}[/itex], [itex]0 \le \theta \le \pi/4[/itex]
- z = [itex]te^{i\pi/4}[/itex], [itex] R \ge t \ge 0[/itex]

**The attempt at a solution**

I'm stumped because I don't know how to evaluate integrals of the form [itex]e^{iz^2}[/itex]. How would I do this?