# Toronto Math Forum

## MAT334--2020S => MAT334--Lectures & Home Assignments => Chapter 2 => Topic started by: Yan Zhou on February 10, 2020, 07:22:49 PM

Title: 2.3 question 3
Post by: Yan Zhou on February 10, 2020, 07:22:49 PM
$$\int_{|z+1| = 2} \frac{zdz}{4-z^{2}} = \int_{|z+1| = 2} \frac{\frac{zdz}{2-z}}{2+z}$$
Since -2 lies in $|z+1| = 2$, Cauchy theorem gives that
$$\frac{1}{2\pi i} \int_{|z+1| = 2} \frac{\frac{zdz}{2-z}}{z-(-2)} = \frac{-2}{2-(-2)} = -\frac{1}{2}$$
then $$\int_{|z+1| = 2} \frac{zdz}{4-z^{2}} = -\pi i$$
However, I checked the answer of textbook and it says the answer is $2\pi i$, I am confused about where i did wrong.
Title: Re: 2.3 question 3
Post by: Yan Zhou on February 10, 2020, 07:46:22 PM
I see. The question on the home assignment is a little bit different from the textbook.
Title: Re: 2.3 question 3
Post by: Yan Zhou on February 10, 2020, 08:11:40 PM
I found some differences between textbook and home assignment, some of them are typos, and some do not affect the questions but the answers. Should we always follow the questions on the textbook?
Title: Re: 2.3 question 3
Post by: Victor Ivrii on February 11, 2020, 07:37:38 AM
Your answer is correct ($-\pi i$).

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