Simplify (5 square root of -1)(-5 square root of 16)

$(5 \sqrt{- 1}) (- 5 \sqrt{16})$

Rewrite $\sqrt{- 1}$ as $i$ .

$5 i (- 5 \sqrt{16})$

Rewrite $16$ as $4^{2}$ .

$5 i (- 5 \sqrt{4^{2}})$

Pull terms out from under the radical, assuming positive real numbers.

$5 i (- 5 \cdot 4)$

Multiply $- 5$ by $4$ .

$5 i \cdot - 20$

Multiply $- 20$ by $5$ .

$- 100 i$