Rouche's Theorem
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Use Rouche's Theorem to determine the number of zeros, counting multiplicities, of the polynomials inside the given regions.
a) z^4 + 3z^3 + 6 inside the circle |z| = 2
b) 2z^5 - 6z^2 + z + 1 in the annulus 1 <= |z| < 2
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Rouche's Theorem is assessed.
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Dear Student,
WE were looking for the roots "on" the curve |z|=2. So, if there are roots for a given equation, they should have their modulus equal to two. In the case of function f(z)=3z^3, obviously, f(z)=0 cannot have a value for z whose modulus is 2
Use Rouche's Theorem to determine the number of zeros, counting ...
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