Simplify (10-4i)(4-5i)+(-15+20i)

$(10 - 4 i) (4 - 5 i) + (- 15 + 20 i)$

Step 1

Remove parentheses.

$(10 - 4 i) (4 - 5 i) - 15 + 20 i$

Step 2

Simplify each term.

Expand $(10 - 4 i) (4 - 5 i)$ using the FOIL Method.

Apply the distributive property.

$10 (4 - 5 i) - 4 i (4 - 5 i) - 15 + 20 i$

Apply the distributive property.

$10 \cdot 4 + 10 (- 5 i) - 4 i (4 - 5 i) - 15 + 20 i$

Apply the distributive property.

$10 \cdot 4 + 10 (- 5 i) - 4 i \cdot 4 - 4 i (- 5 i) - 15 + 20 i$

Simplify and combine like terms.

Simplify each term.

Multiply $10$ by $4$ .

$40 + 10 (- 5 i) - 4 i \cdot 4 - 4 i (- 5 i) - 15 + 20 i$

Multiply $- 5$ by $10$ .

$40 - 50 i - 4 i \cdot 4 - 4 i (- 5 i) - 15 + 20 i$

Multiply $4$ by $- 4$ .

$40 - 50 i - 16 i - 4 i (- 5 i) - 15 + 20 i$

Multiply $- 4 i (- 5 i)$ .

Multiply $- 5$ by $- 4$ .

$40 - 50 i - 16 i + 20 i i - 15 + 20 i$

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

$40 - 50 i - 16 i + 20 (i^{1} i) - 15 + 20 i$

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

$40 - 50 i - 16 i + 20 (i^{1} i^{1}) - 15 + 20 i$

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

$40 - 50 i - 16 i + 20 i^{1 + 1} - 15 + 20 i$

Add $1$ and $1$ .

$40 - 50 i - 16 i + 20 i^{2} - 15 + 20 i$

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

$40 - 50 i - 16 i + 20 \cdot - 1 - 15 + 20 i$

Multiply $20$ by $- 1$ .

$40 - 50 i - 16 i - 20 - 15 + 20 i$

Subtract $20$ from $40$ .

$20 - 50 i - 16 i - 15 + 20 i$

Subtract $16 i$ from $- 50 i$ .

$20 - 66 i - 15 + 20 i$

Step 3

Simplify by adding terms.

Subtract $15$ from $20$ .

$5 - 66 i + 20 i$

Add $- 66 i$ and $20 i$ .

$5 - 46 i$

Simplify (10-4i)(4-5i)+(-15+20i)

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