Simplify (10-3i)(3-10i)

$(10 - 3 i) (3 - 10 i)$

Step 1

Expand $(10 - 3 i) (3 - 10 i)$ using the FOIL Method.

Apply the distributive property.

$10 (3 - 10 i) - 3 i (3 - 10 i)$

Apply the distributive property.

$10 \cdot 3 + 10 (- 10 i) - 3 i (3 - 10 i)$

Apply the distributive property.

$10 \cdot 3 + 10 (- 10 i) - 3 i \cdot 3 - 3 i (- 10 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $10$ by $3$ .

$30 + 10 (- 10 i) - 3 i \cdot 3 - 3 i (- 10 i)$

Multiply $- 10$ by $10$ .

$30 - 100 i - 3 i \cdot 3 - 3 i (- 10 i)$

Multiply $3$ by $- 3$ .

$30 - 100 i - 9 i - 3 i (- 10 i)$

Multiply $- 3 i (- 10 i)$ .

Multiply $- 10$ by $- 3$ .

$30 - 100 i - 9 i + 30 i i$

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

$30 - 100 i - 9 i + 30 (i^{1} i)$

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

$30 - 100 i - 9 i + 30 (i^{1} i^{1})$

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

$30 - 100 i - 9 i + 30 i^{1 + 1}$

Add $1$ and $1$ .

$30 - 100 i - 9 i + 30 i^{2}$

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

$30 - 100 i - 9 i + 30 \cdot - 1$

Multiply $30$ by $- 1$ .

$30 - 100 i - 9 i - 30$

Subtract $30$ from $30$ .

$0 - 100 i - 9 i$

Subtract $100 i$ from $0$ .

$- 100 i - 9 i$

Subtract $9 i$ from $- 100 i$ .

$- 109 i$