Simplify (i+3)+i(2i-4)

$(i + 3) + i (2 i - 4)$

Step 1

Simplify each term.

Apply the distributive property.

$i + 3 + i (2 i) + i \cdot - 4$

Multiply $i (2 i)$ .

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

$i + 3 + 2 (i^{1} i) + i \cdot - 4$

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

$i + 3 + 2 (i^{1} i^{1}) + i \cdot - 4$

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

$i + 3 + 2 i^{1 + 1} + i \cdot - 4$

Add $1$ and $1$ .

$i + 3 + 2 i^{2} + i \cdot - 4$

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

$i + 3 + 2 i^{2} - 4 \cdot i$

Simplify each term.

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

$i + 3 + 2 \cdot - 1 - 4 \cdot i$

Multiply $2$ by $- 1$ .

$i + 3 - 2 - 4 i$

Step 2

Simplify by adding terms.

Subtract $4 i$ from $i$ .

$3 - 2 - 3 i$

Subtract $2$ from $3$ .

$1 - 3 i$