Algebra Examples

4 i + (8 - 3 i) - (12 + \sqrt{- 25})

$4 i + (8 - 3 i) - (12 + \sqrt{- 25})$

Step 1

Remove parentheses.

4 i + 8 - 3 i - (12 + \sqrt{- 25})

$4 i + 8 - 3 i - (12 + \sqrt{- 25})$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Rewrite

- 25

$- 25$ as

- 1 (25)

$- 1 (25)$ .

4 i + 8 - 3 i - (12 + \sqrt{- 1 (25)})

$4 i + 8 - 3 i - (12 + \sqrt{- 1 (25)})$

Step 2.2

Rewrite

\sqrt{- 1 (25)}

$\sqrt{- 1 (25)}$ as

\sqrt{- 1} \cdot \sqrt{25}

$\sqrt{- 1} \cdot \sqrt{25}$ .

4 i + 8 - 3 i - (12 + \sqrt{- 1} \cdot \sqrt{25})

$4 i + 8 - 3 i - (12 + \sqrt{- 1} \cdot \sqrt{25})$

Step 2.3

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

4 i + 8 - 3 i - (12 + i \cdot \sqrt{25})

$4 i + 8 - 3 i - (12 + i \cdot \sqrt{25})$

Step 2.4

Simplify each term.

Tap for more steps...

Step 2.4.1

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

4 i + 8 - 3 i - (12 + i \cdot \sqrt{5^{2}})

$4 i + 8 - 3 i - (12 + i \cdot \sqrt{5^{2}})$

Step 2.4.2

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

4 i + 8 - 3 i - (12 + i \cdot 5)

$4 i + 8 - 3 i - (12 + i \cdot 5)$

Step 2.4.3

Move

5

$5$ to the left of

i

$i$ .

4 i + 8 - 3 i - (12 + 5 i)

$4 i + 8 - 3 i - (12 + 5 i)$

4 i + 8 - 3 i - (12 + 5 i)

$4 i + 8 - 3 i - (12 + 5 i)$

Step 2.5

Apply the distributive property.

4 i + 8 - 3 i - 1 \cdot 12 - (5 i)

$4 i + 8 - 3 i - 1 \cdot 12 - (5 i)$

Step 2.6

Multiply

- 1

$- 1$ by

12

$12$ .

4 i + 8 - 3 i - 12 - (5 i)

$4 i + 8 - 3 i - 12 - (5 i)$

Step 2.7

Multiply

5

$5$ by

- 1

$- 1$ .

4 i + 8 - 3 i - 12 - 5 i

$4 i + 8 - 3 i - 12 - 5 i$

4 i + 8 - 3 i - 12 - 5 i

$4 i + 8 - 3 i - 12 - 5 i$

Step 3

Simplify by adding terms.

Tap for more steps...

Step 3.1

Subtract

3 i

$3 i$ from

4 i

$4 i$ .

8 + i - 12 - 5 i

$8 + i - 12 - 5 i$

Step 3.2

Subtract

12

$12$ from

8

$8$ .

- 4 + i - 5 i

$- 4 + i - 5 i$

Step 3.3

Subtract

5 i

$5 i$ from

i

$i$ .

- 4 - 4 i

$- 4 - 4 i$

- 4 - 4 i

$- 4 - 4 i$