Simplify (1+i)(i+2)

$(1 + i) (i + 2)$

Step 1

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

Apply the distributive property.

$1 (i + 2) + i (i + 2)$

Apply the distributive property.

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

Apply the distributive property.

$1 i + 1 \cdot 2 + i i + i \cdot 2$

$1 i + 1 \cdot 2 + i i + i \cdot 2$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $i$ by $1$ .

$i + 1 \cdot 2 + i i + i \cdot 2$

Multiply $2$ by $1$ .

$i + 2 + i i + i \cdot 2$

Multiply $i i$ .

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

$i + 2 + i^{1} i + i \cdot 2$

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

$i + 2 + i^{1} i^{1} + i \cdot 2$

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

$i + 2 + i^{1 + 1} + i \cdot 2$

Add $1$ and $1$ .

$i + 2 + i^{2} + i \cdot 2$

$i + 2 + i^{2} + i \cdot 2$

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

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

Move $2$ to the left of $i$ .

$i + 2 - 1 + 2 i$

$i + 2 - 1 + 2 i$

Add $i$ and $2 i$ .

$2 - 1 + 3 i$

Subtract $1$ from $2$ .

$1 + 3 i$

$1 + 3 i$

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