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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $5$ .

$15 + 3 i - 2 i \cdot 5 - 2 i i$

Multiply $5$ by $- 2$ .

$15 + 3 i - 10 i - 2 i i$

Multiply $- 2 i i$ .

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

$15 + 3 i - 10 i - 2 (i^{1} i)$

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

$15 + 3 i - 10 i - 2 (i^{1} i^{1})$

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

$15 + 3 i - 10 i - 2 i^{1 + 1}$

Add $1$ and $1$ .

$15 + 3 i - 10 i - 2 i^{2}$

$15 + 3 i - 10 i - 2 i^{2}$

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

$15 + 3 i - 10 i - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$15 + 3 i - 10 i + 2$

$15 + 3 i - 10 i + 2$

Add $15$ and $2$ .

$17 + 3 i - 10 i$

Subtract $10 i$ from $3 i$ .

$17 - 7 i$

$17 - 7 i$

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