Basic Math Examples

$(- 7 + 9 i) (- 7 - 5 i)$

Step 1

Expand $(- 7 + 9 i) (- 7 - 5 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$- 7 (- 7 - 5 i) + 9 i (- 7 - 5 i)$

Step 1.2

Apply the distributive property.

$- 7 \cdot - 7 - 7 (- 5 i) + 9 i (- 7 - 5 i)$

Step 1.3

Apply the distributive property.

$- 7 \cdot - 7 - 7 (- 5 i) + 9 i \cdot - 7 + 9 i (- 5 i)$

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 $- 7$ by $- 7$ .

$49 - 7 (- 5 i) + 9 i \cdot - 7 + 9 i (- 5 i)$

Step 2.1.2

Multiply $- 5$ by $- 7$ .

$49 + 35 i + 9 i \cdot - 7 + 9 i (- 5 i)$

Step 2.1.3

Multiply $- 7$ by $9$ .

$49 + 35 i - 63 i + 9 i (- 5 i)$

Step 2.1.4

Multiply $9 i (- 5 i)$ .

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Step 2.1.4.1

Multiply $- 5$ by $9$ .

$49 + 35 i - 63 i - 45 i i$

Step 2.1.4.2

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

$49 + 35 i - 63 i - 45 (i^{1} i)$

Step 2.1.4.3

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

$49 + 35 i - 63 i - 45 (i^{1} i^{1})$

Step 2.1.4.4

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

$49 + 35 i - 63 i - 45 i^{1 + 1}$

Step 2.1.4.5

Add $1$ and $1$ .

$49 + 35 i - 63 i - 45 i^{2}$

Step 2.1.5

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

$49 + 35 i - 63 i - 45 \cdot - 1$

Step 2.1.6

Multiply $- 45$ by $- 1$ .

$49 + 35 i - 63 i + 45$

Step 2.2

Add $49$ and $45$ .

$94 + 35 i - 63 i$

Step 2.3

Subtract $63 i$ from $35 i$ .

$94 - 28 i$