Precalculus Examples

$(18 - 11 i) - (2 + \sqrt{- 64})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 64$ as $- 1 (64)$ .

$18 - 11 i - (2 + \sqrt{- 1 (64)})$

Step 1.2

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$18 - 11 i - (2 + \sqrt{- 1} \cdot \sqrt{64})$

Step 1.3

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

$18 - 11 i - (2 + i \cdot \sqrt{64})$

Step 1.4

Simplify each term.

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Step 1.4.1

Rewrite $64$ as $8^{2}$ .

$18 - 11 i - (2 + i \cdot \sqrt{8^{2}})$

Step 1.4.2

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

$18 - 11 i - (2 + i \cdot 8)$

Step 1.4.3

Move $8$ to the left of $i$ .

$18 - 11 i - (2 + 8 i)$

Step 1.5

Apply the distributive property.

$18 - 11 i - 1 \cdot 2 - (8 i)$

Step 1.6

Multiply $- 1$ by $2$ .

$18 - 11 i - 2 - (8 i)$

Step 1.7

Multiply $8$ by $- 1$ .

$18 - 11 i - 2 - 8 i$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2$ from $18$ .

$16 - 11 i - 8 i$

Step 2.2

Subtract $8 i$ from $- 11 i$ .

$16 - 19 i$