MAA 4402 Midterm: complex-exam2-sol-fall2013
31 Jan 2019
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Maa 4402 - fall 201 - exaiv. i 2. Show all work should be rvritten in a proper and coherent student in the cla,ss can follow your work. No calcula: [8 pts] suppose f (z) is analytic on a domain d. D if f (z) is real-r,alued for ail z tn d: [8 +-6 : 14 pts] (a) prove thlat if o(r, g) and v(r,il are harmonic. D, then ull,,r,y) a:nd 7(r, g) can differ at most (b) let u(r,y)t: 12 --a2 +2a. show that u(r,g) is conjugal;e u(r,a) of u(r,y). On what domain d is log(z) (b) assumirlg that log(z) is analytic on ,d, show. [2+6:8pt;s] (a) define cos(z). (b) solve the equatio. n working and reasoning. Your hion, and in a way that any rs allowed. :)n ze d. fir,os1r1: [6 pts] let; c" be ther straight-line segment from the contour integrai. Jc: [6 pts] let c be th. e arc of the circle lzl : 2 ( z:2 lo z:22.
