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# The complex function f(z) = 1/(z^4 - 1) has poles at +-1 and +-i, which may...

The complex function f(z) = 1/(z^4 - 1) has poles at +-1 and +-i, which may or may not contribute to the closed curve integral around C of f(z)dz. In turn, the closed curve C that you use depends on the 2nd letter of your first name! Specifically, convert that letter to its numerical position in the Roman alphabet (A=1, B=2, ..., Z=26), then divide by 4. Don't worry about fractions, just save the REMAINDER which will be an integer 0, 1, 2, or 3 (this is called Modular Arithmetic and is a very big area of math, but not in 422). If your remainder is 0 then your contour is C0, which is the unit circle centered at z=1 in the complex plane. If your remainder is 1 your contour is C1 the unit circle around i, C2 = unit circle around -1, and C3 = unit circle around -i. All contours are in the widdershins direction, as usual. I would like you to calculate integral_C f(z)dz around your personal circle.

The 2nd letter: h

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