Circle either True or False in each problem below. No justification is necessary

Question

Circle either True or False in each problem below. No justification is necessary. TRUE or FALSE: Log(z^3) = 3Log(z) for all nonzero complex numbers z. TRUE or FALSE: The function e1/z has an essential singularity at 0. TRUE or FALSE: If a complex function of a complex variable f(z) is analytic at 8 - i then f'(z) must be analytic at 8 - i. TRUE or FALSE: Let C and Q be any two contours from -4 + i to 7 + 5i which lie entirely in the upper half plane, y > 0, then integral_C e^z^4Log(z)/z-2i dz = integral_Q e^z^4Log(z)/z-2i dz. TRUE or FALSE: Let C_R denote the positively oriented circle centered at 0 of radius R then integral_C20000 z^2(z - 3i)/(z^20 + i)(z^2 + 3)1000 dz= integral_C1/25z^-4(z^-1-3i)/(z^-20+i)(z^-2 + 3)1000 dz TRUE or FALSE: The only fractional linear transformations T(z) such that T(infinity) = infinity are those of the form T(z) = alphaz + beta where alpha, beta are any complex numbers such that alpha notequalto 0.

Explanation / Answer

a. TRUE

b. TRUE

c. TRUE

d. False

e. False

f. TRUE

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