Precalculus Examples

$(4 - 9 i) (- 7 + 5 i)$

Step 1

Expand $(4 - 9 i) (- 7 + 5 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$4 (- 7 + 5 i) - 9 i (- 7 + 5 i)$

Step 1.2

Apply the distributive property.

$4 \cdot - 7 + 4 (5 i) - 9 i (- 7 + 5 i)$

Step 1.3

Apply the distributive property.

$4 \cdot - 7 + 4 (5 i) - 9 i \cdot - 7 - 9 i (5 i)$

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 $4$ by $- 7$ .

$- 28 + 4 (5 i) - 9 i \cdot - 7 - 9 i (5 i)$

Step 2.1.2

Multiply $5$ by $4$ .

$- 28 + 20 i - 9 i \cdot - 7 - 9 i (5 i)$

Step 2.1.3

Multiply $- 7$ by $- 9$ .

$- 28 + 20 i + 63 i - 9 i (5 i)$

Step 2.1.4

Multiply $- 9 i (5 i)$ .

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Step 2.1.4.1

Multiply $5$ by $- 9$ .

$- 28 + 20 i + 63 i - 45 i i$

Step 2.1.4.2

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

$- 28 + 20 i + 63 i - 45 (i^{1} i)$

Step 2.1.4.3

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

$- 28 + 20 i + 63 i - 45 (i^{1} i^{1})$

Step 2.1.4.4

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

$- 28 + 20 i + 63 i - 45 i^{1 + 1}$

Step 2.1.4.5

Add $1$ and $1$ .

$- 28 + 20 i + 63 i - 45 i^{2}$

Step 2.1.5

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

$- 28 + 20 i + 63 i - 45 \cdot - 1$

Step 2.1.6

Multiply $- 45$ by $- 1$ .

$- 28 + 20 i + 63 i + 45$

Step 2.2

Add $- 28$ and $45$ .

$17 + 20 i + 63 i$

Step 2.3

Add $20 i$ and $63 i$ .

$17 + 83 i$