complex analysis exam 2018.pdf - •> fc ~ o•~ ~ ·~-�:r'·~ ·•.•:f111.lt • 4~-4 ~_e • KENYATTA UNIVERSITY UNIVERSITY EXAMINATIONS 2017/2018

complex analysis exam 2018.pdf - •> fc ~ o•~ ~...

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,/''.'! >'\(: fc ~o •~ - ~ , ·~";-·:r'·~- ·• :.•,::f111'..lt .. -.: ., .. - ~ . ,. ... 4~\ -- 4!'" .. _e KENYATTA UNIVERSITY UNIVERSITY EXAMINATIONS 2017/2018 FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE IN ELECTRICAL ENGINEERING EEE 402: COMPLEX ANALYSIS FOR ELECTRICAL ENGINEERS DATE: Friday 23 rd February 2018 TIME: 2.00p.m - 4.00p.m INSTRUCTIONS: Answer question ONE and any other two Question One (30 marks) ,, a). Define the following terms i. A simply connected region 11. A singular point d'f a complex function b ). Test the continuity of a complex function { z 2 +16 4 . , z-:;/:. l f(z)= z-4i 8i , z = 4i . c ). Find all the fifth roots of the following complex number -4+4i (1 mark) (1 marks) (3 marks) (5 marks) d) . Evaluate J z - l · dz using Residue theorem, where C : jz - ij = 2 . c(z+1)2(z-2) e). (5 marks) If w = <f> + ilfl represent a co2!J?lex potential for ao electric field and ( - . lfl(x, y) = 2y - 3x 2 }' + y 3 _ .Determine the function ¢(x, y), . Express f (z) m terms of z - -- --- ·-· ·- - ~ (5 marks) INVOLVEMENT IN ANY EXAMINATION IRREGULARITY SHALL LEAD TO DISCONTINUATION Page 1 of 3
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