MTH305 : Complex Analysis II (2018)

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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