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Let \(z\) be a complex number such that \(|z| = 1. \) Find the largest possible value of \(|z^2 + z - 1|.\)
 

 Mar 22, 2022
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If |z| = 1, then z could be 1 and -1. 

We can see there are multiple possible values of z. 

First plugging in 1 to the quadratic, we end up with |1 + 1 - 1| = 1

Plugging in -1 to the quadratic, we end up with |1 - 1 - 1| = 1 

As you can see, the only value of |z^2 + z - 1| is 1.

Thus,

 

The largest possible value of \(|z^2 + z - 1|\) is 1.

 

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 Mar 24, 2022

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