Simplify i(3-2i)+(1+4i)

$i (3 - 2 i) + (1 + 4 i)$

Remove parentheses.

$i (3 - 2 i) + 1 + 4 i$

Simplify each term.

Apply the distributive property.

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

Move $3$ to the left of $i$ .

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

Multiply $i (- 2 i)$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

Simplify each term.

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

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

Multiply $- 2$ by $- 1$ .

$3 i + 2 + 1 + 4 i$

Simplify by adding terms.

Add $3 i$ and $4 i$ .

$2 + 1 + 7 i$

Add $2$ and $1$ .

$3 + 7 i$