(3) [10 Marks] Determine whether the statement made is always true or some times false. Jus- tify your answers in all ca

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3 10 Marks Determine Whether The Statement Made Is Always True Or Some Times False Jus Tify Your Answers In All Ca 1 (41.2 KiB) Viewed 27 times

(3) [10 Marks] Determine whether the statement made is always true or some times false. Jus- tify your answers in all cases. (a) For each complex number z, arg( 7 ) = arg(-). arg-). (b) The contour integral ſe (e? + cosh z) dz is independent of contour C. (c) For each complex number z, sinh z = -i sin(iz). (d) If the functions f and g have a pole at zo, then the function f + g has a pole at zo. 1+i (e) Suppose the function f(x) = — is expanded in Taylor series centered at zo = 1 + 3i. 2-i Then the radius of convergence of the series is R = V2.