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**Test 4 / Spring 2020 Test 2 Monday Sitting Problem 3**

« **on:**December 01, 2020, 01:42:57 PM »

f(z) = (z$^4$ -$\pi^4$)tan$^2$($\frac{z}{2}$)

Part b of this question is asking to determine the types of the singular point.

In solution, it says z=2n$\pi$ with n$\neq$ $\pm$ 1 are double zeros; z=(2n+1)$\pi$ with n$\neq$ $\pm$ 1 are double poles.

Could anyone explain why n$\neq$ $\pm$ 1 here? Why is not n$\neq$ -1, 0?

Thanks in advanced!

Part b of this question is asking to determine the types of the singular point.

In solution, it says z=2n$\pi$ with n$\neq$ $\pm$ 1 are double zeros; z=(2n+1)$\pi$ with n$\neq$ $\pm$ 1 are double poles.

Could anyone explain why n$\neq$ $\pm$ 1 here? Why is not n$\neq$ -1, 0?

Thanks in advanced!