1. The problem is to simplify the expression $-13 + \sqrt{-100}$.\n\n2. Recall that the square root of a negative number involves imaginary numbers. Specifically, $\sqrt{-a} = i\sqrt{a}$ where $i$ is the imaginary unit with the property $i^2 = -1$.\n\n3. Apply this rule to $\sqrt{-100}$: $$\sqrt{-100} = i\sqrt{100} = 10i.$$\n\n4. Substitute back into the original expression: $$-13 + \sqrt{-100} = -13 + 10i.$$\n\n5. The simplified form is a complex number with a real part $-13$ and an imaginary part $10i$.