Evaluate 5i(-7+6i)

$5 i (- 7 + 6 i)$

Step 1

Apply the distributive property.

$5 i \cdot - 7 + 5 i (6 i)$

Step 2

Multiply $- 7$ by $5$ .

$- 35 i + 5 i (6 i)$

Step 3

Multiply $5 i (6 i)$ .

Multiply $6$ by $5$ .

$- 35 i + 30 i i$

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

$- 35 i + 30 (i^{1} i)$

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

$- 35 i + 30 (i^{1} i^{1})$

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

$- 35 i + 30 i^{1 + 1}$

Add $1$ and $1$ .

$- 35 i + 30 i^{2}$

Step 4

Simplify each term.

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

$- 35 i + 30 \cdot - 1$

Multiply $30$ by $- 1$ .

$- 35 i - 30$

Step 5

Reorder $- 35 i$ and $- 30$ .

$- 30 - 35 i$