Simplify (4+i)^2

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

Step 1

Rewrite ${(4 + i)}^{2}$ as $(4 + i) (4 + i)$ .

$(4 + i) (4 + i)$

Step 2

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

Apply the distributive property.

$4 (4 + i) + i (4 + i)$

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 i + i \cdot 4 + i i$

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

$16 + 4 i + 4 \cdot i + i i$

Multiply $i i$ .

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

$16 + 4 i + 4 i + i^{1} i$

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

$16 + 4 i + 4 i + i^{1} i^{1}$

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

$16 + 4 i + 4 i + i^{1 + 1}$

Add $1$ and $1$ .

$16 + 4 i + 4 i + i^{2}$

$16 + 4 i + 4 i + i^{2}$

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

$16 + 4 i + 4 i - 1$

$16 + 4 i + 4 i - 1$

Subtract $1$ from $16$ .

$15 + 4 i + 4 i$

Add $4 i$ and $4 i$ .

$15 + 8 i$

$15 + 8 i$

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