Simplify 2i(7+3i)+5(-5i)

$2 i (7 + 3 i) + 5 (- 5 i)$

Step 1

Simplify each term.

Apply the distributive property.

$2 i \cdot 7 + 2 i (3 i) + 5 (- 5 i)$

Multiply $7$ by $2$ .

$14 i + 2 i (3 i) + 5 (- 5 i)$

Multiply $2 i (3 i)$ .

Multiply $3$ by $2$ .

$14 i + 6 i i + 5 (- 5 i)$

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

$14 i + 6 (i^{1} i) + 5 (- 5 i)$

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

$14 i + 6 (i^{1} i^{1}) + 5 (- 5 i)$

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

$14 i + 6 i^{1 + 1} + 5 (- 5 i)$

Add $1$ and $1$ .

$14 i + 6 i^{2} + 5 (- 5 i)$

Simplify each term.

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

$14 i + 6 \cdot - 1 + 5 (- 5 i)$

Multiply $6$ by $- 1$ .

$14 i - 6 + 5 (- 5 i)$

Multiply $- 5$ by $5$ .

$14 i - 6 - 25 i$

Step 2

Subtract $25 i$ from $14 i$ .

$- 6 - 11 i$