Zeroing out, part 3

Algebra Level 3

Let z z be a complex number.

Consider the equation ( z 3 − 1 ) / ( z 2 + z − 2 ) (z^3 - 1) / (z^2 + z - 2) on the complex plane. How many zeroes does it have?

3 2 0 1

Denton Young by Denton Young , 47, USA

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1 solution

Denton Young
Feb 5, 2016

Factoring: ( z − 1 ) ( z 2 + z + 1 ) / ( z − 1 ) ( z + 2 ) (z-1)(z^2 + z + 1) / (z-1)(z+2)

0/0 at z = 1. That is not a valid zero. The other two complex zeroes are valid, so it has two zeroes and one removable singularity.

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