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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $3$ .

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

Multiply $3$ by $- 2$ .

$15 + 5 i - 6 i - 2 i i$

Multiply $- 2 i i$ .

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

$15 + 5 i - 6 i - 2 (i^{1} i)$

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

$15 + 5 i - 6 i - 2 (i^{1} i^{1})$

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

$15 + 5 i - 6 i - 2 i^{1 + 1}$

Add $1$ and $1$ .

$15 + 5 i - 6 i - 2 i^{2}$

$15 + 5 i - 6 i - 2 i^{2}$

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

$15 + 5 i - 6 i - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$15 + 5 i - 6 i + 2$

$15 + 5 i - 6 i + 2$

Add $15$ and $2$ .

$17 + 5 i - 6 i$

Subtract $6 i$ from $5 i$ .

$17 - i$

$17 - i$

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