#### Answer

$\frac{1}{4}$

#### Work Step by Step

To make the expression,
$z^2+z$
a perfect square trinomial, we would have to add half of the coefficient of the b term squared to the expression.
($\frac{1}{2}\cdot 1)^2=(\frac{1}{2})^2=\frac{1}{4}$
$z^2+z+\frac{1}{4}$