Write in Standard Form (7-5i)(2+3i)

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

Step 1

Expand $(7 - 5 i) (2 + 3 i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $7$ by $2$ .

$14 + 7 (3 i) - 5 i \cdot 2 - 5 i (3 i)$

Multiply $3$ by $7$ .

$14 + 21 i - 5 i \cdot 2 - 5 i (3 i)$

Multiply $2$ by $- 5$ .

$14 + 21 i - 10 i - 5 i (3 i)$

Multiply $- 5 i (3 i)$ .

Multiply $3$ by $- 5$ .

$14 + 21 i - 10 i - 15 i i$

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

$14 + 21 i - 10 i - 15 (i^{1} i)$

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

$14 + 21 i - 10 i - 15 (i^{1} i^{1})$

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

$14 + 21 i - 10 i - 15 i^{1 + 1}$

Add $1$ and $1$ .

$14 + 21 i - 10 i - 15 i^{2}$

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

$14 + 21 i - 10 i - 15 \cdot - 1$

Multiply $- 15$ by $- 1$ .

$14 + 21 i - 10 i + 15$

Add $14$ and $15$ .

$29 + 21 i - 10 i$

Subtract $10 i$ from $21 i$ .

$29 + 11 i$