Simplify 2i(5-3i)

$2 i (5 - 3 i)$

Step 1

Apply the distributive property.

$2 i \cdot 5 + 2 i (- 3 i)$

Step 2

Multiply $5$ by $2$ .

$10 i + 2 i (- 3 i)$

Step 3

Multiply $2 i (- 3 i)$ .

Multiply $- 3$ by $2$ .

$10 i - 6 i i$

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

$10 i - 6 (i^{1} i)$

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

$10 i - 6 (i^{1} i^{1})$

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

$10 i - 6 i^{1 + 1}$

Add $1$ and $1$ .

$10 i - 6 i^{2}$

Step 4

Simplify each term.

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

$10 i - 6 \cdot - 1$

Multiply $- 6$ by $- 1$ .

$10 i + 6$

Step 5

Reorder $10 i$ and $6$ .

$6 + 10 i$