Simplify (2+4i)+i(2+i)

$(2 + 4 i) + i (2 + i)$

Step 1

Simplify each term.

Apply the distributive property.

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

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

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

Multiply $i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

$2 + 4 i + 2 i - 1$

Step 2

Simplify by adding terms.

Subtract $1$ from $2$ .

$1 + 4 i + 2 i$

Add $4 i$ and $2 i$ .

$1 + 6 i$