Let \(z\) be a complex number such that \(|z| = 1. \) Find the largest possible value of \(|z^2 + z - 1|.\)
+1632 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.
