Simplify -6(-4-7i)-(3i)(-i)

$- 6 (- 4 - 7 i) - (3 i) (- i)$

Step 1

Simplify each term.

Apply the distributive property.

$- 6 \cdot - 4 - 6 (- 7 i) - 3 i (- i)$

Multiply $- 6$ by $- 4$ .

$24 - 6 (- 7 i) - 3 i (- i)$

Multiply $- 7$ by $- 6$ .

$24 + 42 i - 3 i (- i)$

Multiply $- 3 i (- i)$ .

Multiply $- 1$ by $- 3$ .

$24 + 42 i + 3 i i$

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

$24 + 42 i + 3 (i^{1} i)$

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

$24 + 42 i + 3 (i^{1} i^{1})$

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

$24 + 42 i + 3 i^{1 + 1}$

Add $1$ and $1$ .

$24 + 42 i + 3 i^{2}$

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

$24 + 42 i + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$24 + 42 i - 3$

Step 2

Subtract $3$ from $24$ .

$21 + 42 i$