Precalculus Examples

$(\sqrt{- 4} + i) (6 - 5 i)$

Step 1

Rewrite $- 4$ as $- 1 (4)$ .

$(\sqrt{- 1 (4)} + i) (6 - 5 i)$

Step 2

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$(\sqrt{- 1} \cdot \sqrt{4} + i) (6 - 5 i)$

Step 3

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

$(i \cdot \sqrt{4} + i) (6 - 5 i)$

Step 4

Simplify each term.

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Step 4.1

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

$(i \cdot \sqrt{2^{2}} + i) (6 - 5 i)$

Step 4.2

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

$(i \cdot 2 + i) (6 - 5 i)$

Step 4.3

Move $2$ to the left of $i$ .

$(2 i + i) (6 - 5 i)$

Step 5

Simplify terms.

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Step 5.1

Add $2 i$ and $i$ .

$3 i (6 - 5 i)$

Step 5.2

Apply the distributive property.

$3 i \cdot 6 + 3 i (- 5 i)$

Step 5.3

Multiply $6$ by $3$ .

$18 i + 3 i (- 5 i)$

Step 6

Multiply $3 i (- 5 i)$ .

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Step 6.1

Multiply $- 5$ by $3$ .

$18 i - 15 i i$

Step 6.2

Raise $i$ to the power of $1$ .

$18 i - 15 (i^{1} i)$

Step 6.3

Raise $i$ to the power of $1$ .

$18 i - 15 (i^{1} i^{1})$

Step 6.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$18 i - 15 i^{1 + 1}$

Step 6.5

Add $1$ and $1$ .

$18 i - 15 i^{2}$

Step 7

Simplify each term.

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Step 7.1

Rewrite $i^{2}$ as $- 1$ .

$18 i - 15 \cdot - 1$

Step 7.2

Multiply $- 15$ by $- 1$ .

$18 i + 15$

Step 8

Reorder $18 i$ and $15$ .

$15 + 18 i$