Multiply (5-3i)(2-8i)

$(5 - 3 i) (2 - 8 i)$

Expand $(5 - 3 i) (2 - 8 i)$ using the FOIL Method.

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Apply the distributive property.

$5 (2 - 8 i) - 3 i (2 - 8 i)$

Apply the distributive property.

$5 \cdot 2 + 5 (- 8 i) - 3 i (2 - 8 i)$

Apply the distributive property.

$5 \cdot 2 + 5 (- 8 i) - 3 i \cdot 2 - 3 i (- 8 i)$

Simplify and combine like terms.

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Simplify each term.

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Multiply $5$ by $2$ .

$10 + 5 (- 8 i) - 3 i \cdot 2 - 3 i (- 8 i)$

Multiply $- 8$ by $5$ .

$10 - 40 i - 3 i \cdot 2 - 3 i (- 8 i)$

Multiply $2$ by $- 3$ .

$10 - 40 i - 6 i - 3 i (- 8 i)$

Multiply $- 3 i (- 8 i)$ .

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Multiply $- 8$ by $- 3$ .

$10 - 40 i - 6 i + 24 i i$

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

$10 - 40 i - 6 i + 24 (i^{1} i)$

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

$10 - 40 i - 6 i + 24 (i^{1} i^{1})$

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

$10 - 40 i - 6 i + 24 i^{1 + 1}$

Add $1$ and $1$ .

$10 - 40 i - 6 i + 24 i^{2}$

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

$10 - 40 i - 6 i + 24 \cdot - 1$

Multiply $24$ by $- 1$ .

$10 - 40 i - 6 i - 24$

Subtract $24$ from $10$ .

$- 14 - 40 i - 6 i$

Subtract $6 i$ from $- 40 i$ .

$- 14 - 46 i$

Multiply (5-3i)(2-8i)

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