Basic Math Examples

$(6 - 8 i) (1 + i) (4 - 7 i)$

Step 1

Expand $(6 - 8 i) (1 + i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(6 (1 + i) - 8 i (1 + i)) (4 - 7 i)$

Step 1.2

Apply the distributive property.

$(6 \cdot 1 + 6 i - 8 i (1 + i)) (4 - 7 i)$

Step 1.3

Apply the distributive property.

$(6 \cdot 1 + 6 i - 8 i \cdot 1 - 8 i i) (4 - 7 i)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $6$ by $1$ .

$(6 + 6 i - 8 i \cdot 1 - 8 i i) (4 - 7 i)$

Step 2.1.2

Multiply $- 8$ by $1$ .

$(6 + 6 i - 8 i - 8 i i) (4 - 7 i)$

Step 2.1.3

Multiply $- 8 i i$ .

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Step 2.1.3.1

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

$(6 + 6 i - 8 i - 8 (i^{1} i)) (4 - 7 i)$

Step 2.1.3.2

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

$(6 + 6 i - 8 i - 8 (i^{1} i^{1})) (4 - 7 i)$

Step 2.1.3.3

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

$(6 + 6 i - 8 i - 8 i^{1 + 1}) (4 - 7 i)$

Step 2.1.3.4

Add $1$ and $1$ .

$(6 + 6 i - 8 i - 8 i^{2}) (4 - 7 i)$

Step 2.1.4

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

$(6 + 6 i - 8 i - 8 \cdot - 1) (4 - 7 i)$

Step 2.1.5

Multiply $- 8$ by $- 1$ .

$(6 + 6 i - 8 i + 8) (4 - 7 i)$

Step 2.2

Add $6$ and $8$ .

$(14 + 6 i - 8 i) (4 - 7 i)$

Step 2.3

Subtract $8 i$ from $6 i$ .

$(14 - 2 i) (4 - 7 i)$

Step 3

Expand $(14 - 2 i) (4 - 7 i)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$14 (4 - 7 i) - 2 i (4 - 7 i)$

Step 3.2

Apply the distributive property.

$14 \cdot 4 + 14 (- 7 i) - 2 i (4 - 7 i)$

Step 3.3

Apply the distributive property.

$14 \cdot 4 + 14 (- 7 i) - 2 i \cdot 4 - 2 i (- 7 i)$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $14$ by $4$ .

$56 + 14 (- 7 i) - 2 i \cdot 4 - 2 i (- 7 i)$

Step 4.1.2

Multiply $- 7$ by $14$ .

$56 - 98 i - 2 i \cdot 4 - 2 i (- 7 i)$

Step 4.1.3

Multiply $4$ by $- 2$ .

$56 - 98 i - 8 i - 2 i (- 7 i)$

Step 4.1.4

Multiply $- 2 i (- 7 i)$ .

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Step 4.1.4.1

Multiply $- 7$ by $- 2$ .

$56 - 98 i - 8 i + 14 i i$

Step 4.1.4.2

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

$56 - 98 i - 8 i + 14 (i^{1} i)$

Step 4.1.4.3

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

$56 - 98 i - 8 i + 14 (i^{1} i^{1})$

Step 4.1.4.4

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

$56 - 98 i - 8 i + 14 i^{1 + 1}$

Step 4.1.4.5

Add $1$ and $1$ .

$56 - 98 i - 8 i + 14 i^{2}$

Step 4.1.5

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

$56 - 98 i - 8 i + 14 \cdot - 1$

Step 4.1.6

Multiply $14$ by $- 1$ .

$56 - 98 i - 8 i - 14$

Step 4.2

Subtract $14$ from $56$ .

$42 - 98 i - 8 i$

Step 4.3

Subtract $8 i$ from $- 98 i$ .

$42 - 106 i$