Complex Variables MA287 : Third & Final Test
Time allowed: 50 minutes
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Q1. [5 marks]
Evaluate
C
ez
dz
z2
where C is the circle |z| = 3 with positive direction.
Q2. [5 marks]
Evaluate
C
e3z
dz
z i
where C is the ellipse
Complex Variables MA287 : Second Test
Time allowed: 50 minutes
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Q1. [5 marks]
For w = f (z) = (1 + z)/(1 z) nd dw/dz and determine where f (z) is non-analytic.
Q2. [5 marks]
Verify that the real and imaginary parts of
Complex Variables MA287 : First Test
Time allowed: 50 minutes
Attempt all ve questions
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Q1. [5 marks]
Four complex numbers z1 , z2 , z3 , z4 are shown, to scale, in the complex plane. They satisfy
the following conditions: z2 = iz1 , z3 = kz1