Simplify (6-4i)(-1+6i)

$(6 - 4 i) (- 1 + 6 i)$

Step 1

Expand $(6 - 4 i) (- 1 + 6 i)$ using the FOIL Method.

Apply the distributive property.

$6 (- 1 + 6 i) - 4 i (- 1 + 6 i)$

Apply the distributive property.

$6 \cdot - 1 + 6 (6 i) - 4 i (- 1 + 6 i)$

Apply the distributive property.

$6 \cdot - 1 + 6 (6 i) - 4 i \cdot - 1 - 4 i (6 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $- 1$ .

$- 6 + 6 (6 i) - 4 i \cdot - 1 - 4 i (6 i)$

Multiply $6$ by $6$ .

$- 6 + 36 i - 4 i \cdot - 1 - 4 i (6 i)$

Multiply $- 1$ by $- 4$ .

$- 6 + 36 i + 4 i - 4 i (6 i)$

Multiply $- 4 i (6 i)$ .

Multiply $6$ by $- 4$ .

$- 6 + 36 i + 4 i - 24 i i$

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

$- 6 + 36 i + 4 i - 24 (i^{1} i)$

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

$- 6 + 36 i + 4 i - 24 (i^{1} i^{1})$

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

$- 6 + 36 i + 4 i - 24 i^{1 + 1}$

Add $1$ and $1$ .

$- 6 + 36 i + 4 i - 24 i^{2}$

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

$- 6 + 36 i + 4 i - 24 \cdot - 1$

Multiply $- 24$ by $- 1$ .

$- 6 + 36 i + 4 i + 24$

Add $- 6$ and $24$ .

$18 + 36 i + 4 i$

Add $36 i$ and $4 i$ .

$18 + 40 i$