Basic Math Examples

$(1 - 2 i) (1 + 3 i)$

Step 1

Expand $(1 - 2 i) (1 + 3 i)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$1 (1 + 3 i) - 2 i (1 + 3 i)$

Step 1.2

Apply the distributive property.

$1 \cdot 1 + 1 (3 i) - 2 i (1 + 3 i)$

Step 1.3

Apply the distributive property.

$1 \cdot 1 + 1 (3 i) - 2 i \cdot 1 - 2 i (3 i)$

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 $1$ by $1$ .

$1 + 1 (3 i) - 2 i \cdot 1 - 2 i (3 i)$

Step 2.1.2

Multiply $3 i$ by $1$ .

$1 + 3 i - 2 i \cdot 1 - 2 i (3 i)$

Step 2.1.3

Multiply $- 2$ by $1$ .

$1 + 3 i - 2 i - 2 i (3 i)$

Step 2.1.4

Multiply $- 2 i (3 i)$ .

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Step 2.1.4.1

Multiply $3$ by $- 2$ .

$1 + 3 i - 2 i - 6 i i$

Step 2.1.4.2

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

$1 + 3 i - 2 i - 6 (i^{1} i)$

Step 2.1.4.3

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

$1 + 3 i - 2 i - 6 (i^{1} i^{1})$

Step 2.1.4.4

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

$1 + 3 i - 2 i - 6 i^{1 + 1}$

Step 2.1.4.5

Add $1$ and $1$ .

$1 + 3 i - 2 i - 6 i^{2}$

Step 2.1.5

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

$1 + 3 i - 2 i - 6 \cdot - 1$

Step 2.1.6

Multiply $- 6$ by $- 1$ .

$1 + 3 i - 2 i + 6$

Step 2.2

Add $1$ and $6$ .

$7 + 3 i - 2 i$

Step 2.3

Subtract $2 i$ from $3 i$ .

$7 + i$