Algebra Examples

$(5 + - 6 i) (2 + 4 i)$

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

$(5 - 6 i) (2 + 4 i)$

Step 2

Expand $(5 - 6 i) (2 + 4 i)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$5 (2 + 4 i) - 6 i (2 + 4 i)$

Step 2.2

Apply the distributive property.

$5 \cdot 2 + 5 (4 i) - 6 i (2 + 4 i)$

Step 2.3

Apply the distributive property.

$5 \cdot 2 + 5 (4 i) - 6 i \cdot 2 - 6 i (4 i)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $5$ by $2$ .

$10 + 5 (4 i) - 6 i \cdot 2 - 6 i (4 i)$

Step 3.1.2

Multiply $4$ by $5$ .

$10 + 20 i - 6 i \cdot 2 - 6 i (4 i)$

Step 3.1.3

Multiply $2$ by $- 6$ .

$10 + 20 i - 12 i - 6 i (4 i)$

Step 3.1.4

Multiply $- 6 i (4 i)$ .

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Step 3.1.4.1

Multiply $4$ by $- 6$ .

$10 + 20 i - 12 i - 24 i i$

Step 3.1.4.2

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

$10 + 20 i - 12 i - 24 (i^{1} i)$

Step 3.1.4.3

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

$10 + 20 i - 12 i - 24 (i^{1} i^{1})$

Step 3.1.4.4

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

$10 + 20 i - 12 i - 24 i^{1 + 1}$

Step 3.1.4.5

Add $1$ and $1$ .

$10 + 20 i - 12 i - 24 i^{2}$

Step 3.1.5

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

$10 + 20 i - 12 i - 24 \cdot - 1$

Step 3.1.6

Multiply $- 24$ by $- 1$ .

$10 + 20 i - 12 i + 24$

Step 3.2

Add $10$ and $24$ .

$34 + 20 i - 12 i$

Step 3.3

Subtract $12 i$ from $20 i$ .

$34 + 8 i$