Evaluate (2+i)^2

${(2 + i)}^{2}$

Step 1

Rewrite ${(2 + i)}^{2}$ as $(2 + i) (2 + i)$ .

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 + 2 i + i \cdot 2 + i i$

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

$4 + 2 i + 2 \cdot i + i i$

Multiply $i i$ .

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

$4 + 2 i + 2 i + i^{1} i$

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

$4 + 2 i + 2 i + i^{1} i^{1}$

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

$4 + 2 i + 2 i + i^{1 + 1}$

Add $1$ and $1$ .

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

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

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

$4 + 2 i + 2 i - 1$

$4 + 2 i + 2 i - 1$

Subtract $1$ from $4$ .

$3 + 2 i + 2 i$

Add $2 i$ and $2 i$ .

$3 + 4 i$

$3 + 4 i$

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