NATIONAL OPEN UNIVERSITY OF NIGERIA
Plot 91, Cadastral Zone, Nnamdi Azikiwe Express Way, Jabi-Abuja
FACULTY OF SCIENCES
January\February Examination 2018
Course Code: MTH305
Course Title: Complex Analysis II
Credit Unit: 3
Time Allowed: 3 Hours
Total Marks: 70%
INSTRUCTION: ANSWER QUESTION ONE(1) AND ANY FOUR (4)
QUESTIONS (TOTAL = 5 QUESTIONS IN ALL)
1(a) Expand f(z) = cos z by taylor series about the point (8marks)
1(b) Show that the following function are harmonic
(i) (3marks)
(ii) (3marks)
1(c) Given that
(3marks)
1(d) Express cos3 and Sin 3 in terms of sin and Cos only and state the real and imaginary parts. (5marks)
Total Marks = 22
(2a) Show that is an hyperbolic function (6marks)
(2b) Find the cube root of 8 in terms of complex number (6marks)
(3a) Verify that the real and imaginary parts of the function satisfy Cauchy-Riemann equation and deduce the analyticity of the function (8marks)
(3b) Prove that (4marks)
(4a) Solve: (6marks)
(4b) List six types of function (6marks)
(5a) Given that (i.e in polar form) Find the modulus of z and the principal argument of z.
(5b) Find also argz, if
(6a) Given that . Find a and b (6marks)
(6 b) If Find:
(3marks)
(3marks)
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