Precalculus Examples

$(5 - 3 i) (1 + i)$

Step 1

Expand $(5 - 3 i) (1 + i)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$5 (1 + i) - 3 i (1 + i)$

Step 1.2

Apply the distributive property.

$5 \cdot 1 + 5 i - 3 i (1 + i)$

Step 1.3

Apply the distributive property.

$5 \cdot 1 + 5 i - 3 i \cdot 1 - 3 i i$

$5 \cdot 1 + 5 i - 3 i \cdot 1 - 3 i i$

Step 2

Simplify and combine like terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Multiply $5$ by $1$ .

$5 + 5 i - 3 i \cdot 1 - 3 i i$

Step 2.1.2

Multiply $- 3$ by $1$ .

$5 + 5 i - 3 i - 3 i i$

Step 2.1.3

Multiply $- 3 i i$ .

Tap for more steps...

Step 2.1.3.1

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

$5 + 5 i - 3 i - 3 (i^{1} i)$

Step 2.1.3.2

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

$5 + 5 i - 3 i - 3 (i^{1} i^{1})$

Step 2.1.3.3

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

$5 + 5 i - 3 i - 3 i^{1 + 1}$

Step 2.1.3.4

Add $1$ and $1$ .

$5 + 5 i - 3 i - 3 i^{2}$

$5 + 5 i - 3 i - 3 i^{2}$

Step 2.1.4

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

$5 + 5 i - 3 i - 3 \cdot - 1$

Step 2.1.5

Multiply $- 3$ by $- 1$ .

$5 + 5 i - 3 i + 3$

$5 + 5 i - 3 i + 3$

Step 2.2

Add $5$ and $3$ .

$8 + 5 i - 3 i$

Step 2.3

Subtract $3 i$ from $5 i$ .

$8 + 2 i$

$8 + 2 i$

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