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Math Help - Need help solving this problem(using cauchy's integral theorem)

  1. #1
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    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.

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  2. #2
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    Draw the circle for C then plot the point z_0 and see that it is inside the circle. Do you not understand how to draw the circle?
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  3. #3
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    No I dont,how do you draw a circle when there is "i"

    Please help me out with that
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  4. #4
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    The equation |z-(a+bi)|=r (where r>0) is a circle centered at (a,b) with radius r. So its equation in rectangular coordinates is (x-a)^2+(y-b)^2= r^2. Does that make sense?
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  5. #5
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    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 ?
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  6. #6
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    Quote Originally Posted by anjay View Post
    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! |z+1-i|=|z-(1+i)|. So where is the center?
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