Simplify 5i(4-7i)

$5 i (4 - 7 i)$

Step 1

Apply the distributive property.

$5 i \cdot 4 + 5 i (- 7 i)$

Step 2

Multiply $4$ by $5$ .

$20 i + 5 i (- 7 i)$

Step 3

Multiply $5 i (- 7 i)$ .

Multiply $- 7$ by $5$ .

$20 i - 35 i i$

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

$20 i - 35 (i^{1} i)$

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

$20 i - 35 (i^{1} i^{1})$

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

$20 i - 35 i^{1 + 1}$

Add $1$ and $1$ .

$20 i - 35 i^{2}$

Step 4

Simplify each term.

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

$20 i - 35 \cdot - 1$

Multiply $- 35$ by $- 1$ .

$20 i + 35$

Step 5

Reorder $20 i$ and $35$ .

$35 + 20 i$