To determine what will make the expression \( y^2 + 25 \) equal to zero, we can set up the equation:
\[ y^2 + 25 = 0 \]
Next, we can isolate \( y^2 \) by subtracting 25 from both sides:
\[ y^2 = -25 \]
To find \( y \), we take the square root of both sides. However, we note that the right side, \(-25\), is a negative number, which leads us to complex numbers:
\[ y = \pm \sqrt{-25} \]
This can be rewritten using imaginary numbers:
\[ y = \pm 5i \]
where \( i \) is the imaginary unit defined as \( i = \sqrt{-1} \).
Thus, the values of \( y \) that make \( y^2 + 25 = 0 \) are:
\[ y = 5i \quad \text{or} \quad y = -5i \]