Simplify 3i(-2i+7)+2(-2-11i)-i

$3 i (- 2 i + 7) + 2 (- 2 - 11 i) - i$

Simplify each term.

Apply the distributive property.

$3 i (- 2 i) + 3 i \cdot 7 + 2 (- 2 - 11 i) - i$

Multiply $3 i (- 2 i)$ .

Multiply $- 2$ by $3$ .

$- 6 i i + 3 i \cdot 7 + 2 (- 2 - 11 i) - i$

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

$- 6 (i^{1} i) + 3 i \cdot 7 + 2 (- 2 - 11 i) - i$

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

$- 6 (i^{1} i^{1}) + 3 i \cdot 7 + 2 (- 2 - 11 i) - i$

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

$- 6 i^{1 + 1} + 3 i \cdot 7 + 2 (- 2 - 11 i) - i$

Add $1$ and $1$ .

$- 6 i^{2} + 3 i \cdot 7 + 2 (- 2 - 11 i) - i$

Multiply $7$ by $3$ .

$- 6 i^{2} + 21 i + 2 (- 2 - 11 i) - i$

Simplify each term.

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

$- 6 \cdot - 1 + 21 i + 2 (- 2 - 11 i) - i$

Multiply $- 6$ by $- 1$ .

$6 + 21 i + 2 (- 2 - 11 i) - i$

Apply the distributive property.

$6 + 21 i + 2 \cdot - 2 + 2 (- 11 i) - i$

Multiply $2$ by $- 2$ .

$6 + 21 i - 4 + 2 (- 11 i) - i$

Multiply $- 11$ by $2$ .

$6 + 21 i - 4 - 22 i - i$

Simplify by adding terms.

Subtract $4$ from $6$ .

$2 + 21 i - 22 i - i$

Subtract $22 i$ from $21 i$ .

$2 - i - i$

Subtract $i$ from $- i$ .

$2 - 2 i$