Simplify 3i(4-5i)-1

$3 i (4 - 5 i) - 1$

Simplify each term.

Apply the distributive property.

$3 i \cdot 4 + 3 i (- 5 i) - 1$

Multiply $4$ by $3$ .

$12 i + 3 i (- 5 i) - 1$

Multiply $3 i (- 5 i)$ .

Multiply $- 5$ by $3$ .

$12 i - 15 i i - 1$

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

$12 i - 15 (i^{1} i) - 1$

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

$12 i - 15 (i^{1} i^{1}) - 1$

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

$12 i - 15 i^{1 + 1} - 1$

Add $1$ and $1$ .

$12 i - 15 i^{2} - 1$

Simplify each term.

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

$12 i - 15 \cdot - 1 - 1$

Multiply $- 15$ by $- 1$ .

$12 i + 15 - 1$

Simplify the expression.

Subtract $1$ from $15$ .

$12 i + 14$

Reorder $12 i$ and $14$ .

$14 + 12 i$