Complex integration over a curve

[af1428]

Homework Statement

Compute ∫_C (z+i)/(z³+2z²) dz

Homework Equations

C is the positively orientated circle |z+2-i|=2

The Attempt at a Solution

I managed to solve a similar problem where the circle was simply |z|=1, with the centre at the origin converting it to z=e^iθ with 0≤θ2∏. I'm not sure how to go forward with the centre in another position.

If I want to parametise the equation for z for the circle, then I get two different equations for z because of the possibility that it could be + or - because of the absolute value.

I haven't gotten very far - could anyone help start me off on this!

 

[HallsofIvy]

|z+ 2- i|= 2 is the same as |z- (-2+ i)|= 2 and is the circle with center at -2+ i and radius 2 with $\theta$ going from 0 to $2\pi$. Yes, we can write the circle with center at 0 and radius 1 as $z= e^{i\theta}$. The circle with center at 0 and radius 2 is $z= 2e^{i\theta}$. Finally, the circle with center -2+ i and radius 2 is $z= -2+ i+ 2e^{i\theta}$

 

[af1428]

Thank you, that helps!