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Complex Analysis

by: Reuben Hudson DDS

Complex Analysis MATH 621

Reuben Hudson DDS
GPA 3.55


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This 2 page Class Notes was uploaded by Reuben Hudson DDS on Friday October 30, 2015. The Class Notes belongs to MATH 621 at University of Massachusetts taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/232229/math-621-university-of-massachusetts in Mathematics (M) at University of Massachusetts.

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Date Created: 10/30/15
MATH 621 7 COMPLEX ANALYSIS Review Problems 1 Compute 2 7i 3i 1 a 74 i2 b c1z100 m i i i 5 i d e f mm 2 In each case sketch the set of points determined by the given condition Argue geometrically Whenever possible a 2 17 2i gt 2 b Rez S Re22 c 2 2 i lt lmz dReIo e z1 271 f ziz7i 4 3 Express in polar form i 7 1 a 390 71 0 713 2 d 4 Let a and b be positive real numbers Prove that tan 1 1 tan 1 L tan 1 l ab a2ab1 a What happens for arbitrary a b real 5 a Prove the following trigonometric identity 1 3 l5 5 6 7 7 7 cos i 32 cos6x 16 cos4x 32 cos2x 16 b Compute the average 1 27r 6 7 cos 27139 0 c Can you generalize this to the average of cos x 0 S x S 27139 6 a Find all roots and represent them geometrically i 4W4 ii 1 fix3V5 b Find the four roots of the equation 24 4 0 and use them to factor 24 4 into quadratic factors With real coef cients 7 Express each of the following in the form uiv Where u and v are real valued functions of two real variables that is compute Mac y Refac iy and 1116 y lmfac iy a f9 122 390 f9 6 6 f9 6 d fz 8 Find all values of 2 such that a ez m2 b ez 3 4i c ez e 13 is d sinz 2 e sinz 0 f cosz 0 g sinhz 0 h coshz 0 9 Compute the following values a sinLogi b LogLogi c eLogH d Log6 4 10 Compute all values of a 1239 b 1i1i Which are the Principal Values


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