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Let f(z) = [ Sin ^2 z . (1+cosz) ] / [ {(z-1)^2}-1 ]
1- find the zeros of f 

2- classify the zero z=0 , z= pi, z=2pi

Dec 20th, 2014

The zeroes of this function are pi and 2pi. 

z = 0 is undefined because 0 is not in the domain of f(z).  It's not in the domain because when you plug 0 into the denominator, you get 0 [(0-1)^2 - 1] = 0.

And I'm not sure why you mean by "classify" the zeroes z = pi and z = 2pi.  The function doesn't cross the x-axis; it just hits the x-axis at these points and then returns up in the positive y-direction.

Dec 21st, 2014

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Dec 20th, 2014
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