Simplify 3i(3-4i)-i(6-5i)

$3 i (3 - 4 i) - i (6 - 5 i)$

Step 1

Simplify each term.

Apply the distributive property.

$3 i \cdot 3 + 3 i (- 4 i) - i (6 - 5 i)$

Multiply $3$ by $3$ .

$9 i + 3 i (- 4 i) - i (6 - 5 i)$

Multiply $3 i (- 4 i)$ .

Multiply $- 4$ by $3$ .

$9 i - 12 i i - i (6 - 5 i)$

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

$9 i - 12 (i^{1} i) - i (6 - 5 i)$

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

$9 i - 12 (i^{1} i^{1}) - i (6 - 5 i)$

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

$9 i - 12 i^{1 + 1} - i (6 - 5 i)$

Add $1$ and $1$ .

$9 i - 12 i^{2} - i (6 - 5 i)$

Simplify each term.

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

$9 i - 12 \cdot - 1 - i (6 - 5 i)$

Multiply $- 12$ by $- 1$ .

$9 i + 12 - i (6 - 5 i)$

Apply the distributive property.

$9 i + 12 - i \cdot 6 - i (- 5 i)$

Multiply $6$ by $- 1$ .

$9 i + 12 - 6 i - i (- 5 i)$

Multiply $- i (- 5 i)$ .

Multiply $- 5$ by $- 1$ .

$9 i + 12 - 6 i + 5 i i$

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

$9 i + 12 - 6 i + 5 (i^{1} i)$

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

$9 i + 12 - 6 i + 5 (i^{1} i^{1})$

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

$9 i + 12 - 6 i + 5 i^{1 + 1}$

Add $1$ and $1$ .

$9 i + 12 - 6 i + 5 i^{2}$

Simplify each term.

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

$9 i + 12 - 6 i + 5 \cdot - 1$

Multiply $5$ by $- 1$ .

$9 i + 12 - 6 i - 5$

Step 2

Simplify by adding terms.

Subtract $6 i$ from $9 i$ .

$12 + 3 i - 5$

Subtract $5$ from $12$ .

$7 + 3 i$

Simplify 3i(3-4i)-i(6-5i)

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