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# Review Sheet for MATH 621 at UMass

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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Massachusetts taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15
MATH 621 7 COMPLEX ANALYSIS Review Problems 1 Compute 27 3i 1 a 4 i2 b c1z100 m i z i5 i C01 13i2 N e 1332 f 1igti 2 In each case sketch the set of points determined by the given condition Argue geometrically Whenever possible a z17 2i gt 2 b Rez S Re22 c 2 2 i lt lmz dReIo e mngzm f zizii 4 3 Express in polar form iii 1ng W71 clti1gt3lt igt2 d i2 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 0 cos6 xdac 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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