Simplify (x+i)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$x \cdot x + x i + i x + i i$

$x \cdot x + x i + i x + i i$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

$x^{2} + x i + i x - 1$

$x^{2} + x i + i x - 1$

Add $x i$ and $i x$ .

Reorder $i$ and $x$ .

$x^{2} + x i + x i - 1$

Add $x i$ and $x i$ .

$x^{2} + 2 x i - 1$

$x^{2} + 2 x i - 1$

$x^{2} + 2 x i - 1$

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