- #1

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## Homework Statement

Determine, by explicit parameterisation,

∫

_{C}dz f(z), where f(z) = z^n , n ∈ Z, n > 0

and C is the line segment from z = 0 to z = 2 together with the line segment from z = 2 to z = 2 + i.

## Homework Equations

∫

_{ϒ}f(z) dz = ∫

_{a}

^{b}dt f(ϒ(t))ϒ'(t) where ϒ'(t)≈dz/dt

## The Attempt at a Solution

Splitting C into two sub contours ϒ

_{1}= {z=x, x ∈ [0 , 2]} and ϒ

_{2}= {z=y, y ∈ [2 , 2+i]}. Then using the equation above to integrate over both and sum. This gave and answer which I really can't gauge whether is correct or not.

(2+i)

^{(n+1)}/(n+1)

But my lecturer gave us a rough check guide and said that if what you start with is a real number then your answer should be real also. Thus am skeptical of my answer.

Any help on the method, answer or general help with this would be greatly appreciated.

Thanks!