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Express both f(z) and f'(z) in terms of the complex variable z=x+iy

a, b∈ R

z=1/(-5-i) in standard (algebraic) form. Further, give an Argand diagram

in which z, z bar and −z are plotted.

1. ∫

C

z

2

z

2 + 2z + 2

where C is the circle |z| = 2.

2. ∫

C

Ln(1−z)dz, where C is the parallelogram with vertices ±i, ±(1+i).

3. ∫ 2π

0

1

1 + 3 cos θ

dθ.

4. ∫

C

z

2

z

4 − 1

dz. where C is the circle |z + 1| = 1

5. ∫

C

e

z

π − i

dz. where C is the unit circle