Simplify (10+i)^2

${(10 + i)}^{2}$

Rewrite ${(10 + i)}^{2}$ as $(10 + i) (10 + i)$ .

$(10 + i) (10 + i)$

Expand $(10 + i) (10 + i)$ using the FOIL Method.

Apply the distributive property.

$10 (10 + i) + i (10 + i)$

Apply the distributive property.

$10 \cdot 10 + 10 i + i (10 + i)$

Apply the distributive property.

$10 \cdot 10 + 10 i + i \cdot 10 + i i$

$10 \cdot 10 + 10 i + i \cdot 10 + i i$

Simplify and combine like terms.

Simplify each term.

Multiply $10$ by $10$ .

$100 + 10 i + i \cdot 10 + i i$

Move $10$ to the left of $i$ .

$100 + 10 i + 10 \cdot i + i i$

Multiply $i i$ .

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

$100 + 10 i + 10 i + i^{1} i$

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

$100 + 10 i + 10 i + i^{1} i^{1}$

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

$100 + 10 i + 10 i + i^{1 + 1}$

Add $1$ and $1$ .

$100 + 10 i + 10 i + i^{2}$

$100 + 10 i + 10 i + i^{2}$

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

$100 + 10 i + 10 i - 1$

$100 + 10 i + 10 i - 1$

Subtract $1$ from $100$ .

$99 + 10 i + 10 i$

Add $10 i$ and $10 i$ .

$99 + 20 i$

$99 + 20 i$

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