# Thread: Need help solving this problem(using cauchy's integral theorem)

1. ## Need help solving this problem(using cauchy's integral theorem)

How is the correct denominator chosen in "1" that I ve pointed.

Can someone elaborate how the conclusion that z0 lies within or outside the circle,and what the presence "i" does to our decision.

2. Draw the circle for $\displaystyle C$ then plot the point $\displaystyle z_0$ and see that it is inside the circle. Do you not understand how to draw the circle?

3. No I dont,how do you draw a circle when there is "i"

4. The equation $\displaystyle |z-(a+bi)|=r$ (where $\displaystyle r>0$) is a circle centered at $\displaystyle (a,b)$ with radius $\displaystyle r$. So its equation in rectangular coordinates is $\displaystyle (x-a)^2+(y-b)^2= r^2$. Does that make sense?

5. So from step 1.

Zo=(-1,2) and Zo=(-1,-2)

Given circle is |z+1-i|,whose center should be z=(-1,1) right?

But in step 2,it says (-1,2) lies within the circle (-1,1),isnt 2 outside the circle ?

6. Originally Posted by anjay
So from step 1.

Zo=(-1,2) and Zo=(-1,-2)

Given circle is |z+1-i|,whose center should be z=(-1,1) right?

But in step 2,it says (-1,2) lies within the circle (-1,1),isnt 2 outside the circle ?
No! $\displaystyle |z+1-i|=|z-(1+i)|$. So where is the center?