Simplify (x+4i)^2

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

$x^{2} + 4 \cdot x i + 4 i x + 4 i (4 i)$

Multiply $4 i (4 i)$ .

Multiply $4$ by $4$ .

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

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

$x^{2} + 4 x i + 4 i x + 16 (i^{1} i)$

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

$x^{2} + 4 x i + 4 i x + 16 (i^{1} i^{1})$

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

$x^{2} + 4 x i + 4 i x + 16 i^{1 + 1}$

Add $1$ and $1$ .

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

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

$x^{2} + 4 x i + 4 i x + 16 \cdot - 1$

Multiply $16$ by $- 1$ .

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

Add $4 x i$ and $4 i x$ .

Move $i$ .

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

Add $4 x i$ and $4 x i$ .

$x^{2} + 8 x i - 16$