Determine the number of zeros and poles inside (counted with multiplicity) of the function z6 sin(TZ)...

 

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Determine the number of zeros and poles inside (counted with multiplicity) of the function z6 sin(TZ) (1 - z²) (2 - z²) (3 — z7) f(z) inside the disc {z: |Z| <4.5} We have that the zeros of the divisor are given as z = 0 (multiplicity 7), z = +1 (multiplicity 1), z = +2 (multiplicity 1), z = ±3, and z = +4. Nevertheless, when z = +1, we have that both the dividend and divisor are equal to zero - and so those two points are neither zeros nor poles. As such, I reckon the number of zeros and poles (counted with multiplicity) inside the disc {z: z <4.5} are 7 +3.2 = 13 and 2 + 7 = 9. Is this a fair argument? Determine the number of zeros and poles inside (counted with multiplicity) of the function z6 sin(TZ) (1 - z²) (2 - z²) (3 — z7) f(z) inside the disc {z: |Z| <4.5} We have that the zeros of the divisor are given as z = 0 (multiplicity 7), z = +1 (multiplicity 1), z = +2 (multiplicity 1), z = ±3, and z = +4. Nevertheless, when z = +1, we have that both the dividend and divisor are equal to zero - and so those two points are neither zeros nor poles. As such, I reckon the number of zeros and poles (counted with multiplicity) inside the disc {z: z <4.5} are 7 +3.2 = 13 and 2 + 7 = 9. Is this a fair argument?

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