Precalculus Examples

$(1 + i) (4 - 3 i)$

Step 1

Expand $(1 + i) (4 - 3 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$1 (4 - 3 i) + i (4 - 3 i)$

Step 1.2

Apply the distributive property.

$1 \cdot 4 + 1 (- 3 i) + i (4 - 3 i)$

Step 1.3

Apply the distributive property.

$1 \cdot 4 + 1 (- 3 i) + i \cdot 4 + i (- 3 i)$

$1 \cdot 4 + 1 (- 3 i) + i \cdot 4 + i (- 3 i)$

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 $1$ .

$4 + 1 (- 3 i) + i \cdot 4 + i (- 3 i)$

Step 2.1.2

Multiply $- 3 i$ by $1$ .

$4 - 3 i + i \cdot 4 + i (- 3 i)$

Step 2.1.3

Move $4$ to the left of $i$ .

$4 - 3 i + 4 \cdot i + i (- 3 i)$

Step 2.1.4

Multiply $i (- 3 i)$ .

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Step 2.1.4.1

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

$4 - 3 i + 4 i - 3 (i^{1} i)$

Step 2.1.4.2

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

$4 - 3 i + 4 i - 3 (i^{1} i^{1})$

Step 2.1.4.3

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

$4 - 3 i + 4 i - 3 i^{1 + 1}$

Step 2.1.4.4

Add $1$ and $1$ .

$4 - 3 i + 4 i - 3 i^{2}$

$4 - 3 i + 4 i - 3 i^{2}$

Step 2.1.5

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

$4 - 3 i + 4 i - 3 \cdot - 1$

Step 2.1.6

Multiply $- 3$ by $- 1$ .

$4 - 3 i + 4 i + 3$

$4 - 3 i + 4 i + 3$

Step 2.2

Add $4$ and $3$ .

$7 - 3 i + 4 i$

Step 2.3

Add $- 3 i$ and $4 i$ .

$7 + i$

$7 + i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$