Simplify 10i-(3- square root of -25)

$10 i - (3 - \sqrt{- 25})$

Step 1

Simplify each term.

Rewrite $- 25$ as $- 1 (25)$ .

$10 i - (3 - \sqrt{- 1 (25)})$

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$10 i - (3 - (\sqrt{- 1} \cdot \sqrt{25}))$

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

$10 i - (3 - (i \cdot \sqrt{25}))$

Simplify each term.

Rewrite $25$ as $5^{2}$ .

$10 i - (3 - (i \cdot \sqrt{5^{2}}))$

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

$10 i - (3 - (i \cdot 5))$

Move $5$ to the left of $i$ .

$10 i - (3 - (5 \cdot i))$

Multiply $5$ by $- 1$ .

$10 i - (3 - 5 i)$

Apply the distributive property.

$10 i - 1 \cdot 3 - (- 5 i)$

Multiply $- 1$ by $3$ .

$10 i - 3 - (- 5 i)$

Multiply $- 5$ by $- 1$ .

$10 i - 3 + 5 i$

Step 2

Add $10 i$ and $5 i$ .

$- 3 + 15 i$