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

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

Simplify each term.

Apply the distributive property.

$5 + 3 i + (- 1 \cdot 5 - (3 i)) (5 - 5 i)$

Multiply $- 1$ by $5$ .

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

Multiply $3$ by $- 1$ .

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $- 5$ by $5$ .

$5 + 3 i - 25 - 5 (- 5 i) - 3 i \cdot 5 - 3 i (- 5 i)$

Multiply $- 5$ by $- 5$ .

$5 + 3 i - 25 + 25 i - 3 i \cdot 5 - 3 i (- 5 i)$

Multiply $5$ by $- 3$ .

$5 + 3 i - 25 + 25 i - 15 i - 3 i (- 5 i)$

Multiply $- 3 i (- 5 i)$ .

Multiply $- 5$ by $- 3$ .

$5 + 3 i - 25 + 25 i - 15 i + 15 i i$

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

$5 + 3 i - 25 + 25 i - 15 i + 15 (i^{1} i)$

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

$5 + 3 i - 25 + 25 i - 15 i + 15 (i^{1} i^{1})$

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

$5 + 3 i - 25 + 25 i - 15 i + 15 i^{1 + 1}$

Add $1$ and $1$ .

$5 + 3 i - 25 + 25 i - 15 i + 15 i^{2}$

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

$5 + 3 i - 25 + 25 i - 15 i + 15 \cdot - 1$

Multiply $15$ by $- 1$ .

$5 + 3 i - 25 + 25 i - 15 i - 15$

Subtract $15$ from $- 25$ .

$5 + 3 i - 40 + 25 i - 15 i$

Subtract $15 i$ from $25 i$ .

$5 + 3 i - 40 + 10 i$

Simplify by adding terms.

Subtract $40$ from $5$ .

$- 35 + 3 i + 10 i$

Add $3 i$ and $10 i$ .

$- 35 + 13 i$

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

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