Simplify (3-4i)(1+5i)-(2-i)

$(3 - 4 i) (1 + 5 i) - (2 - i)$

Simplify each term.

Expand $(3 - 4 i) (1 + 5 i)$ using the FOIL Method.

Apply the distributive property.

$3 (1 + 5 i) - 4 i (1 + 5 i) - (2 - i)$

Apply the distributive property.

$3 \cdot 1 + 3 (5 i) - 4 i (1 + 5 i) - (2 - i)$

Apply the distributive property.

$3 \cdot 1 + 3 (5 i) - 4 i \cdot 1 - 4 i (5 i) - (2 - i)$

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $1$ .

$3 + 3 (5 i) - 4 i \cdot 1 - 4 i (5 i) - (2 - i)$

Multiply $5$ by $3$ .

$3 + 15 i - 4 i \cdot 1 - 4 i (5 i) - (2 - i)$

Multiply $- 4$ by $1$ .

$3 + 15 i - 4 i - 4 i (5 i) - (2 - i)$

Multiply $- 4 i (5 i)$ .

Multiply $5$ by $- 4$ .

$3 + 15 i - 4 i - 20 i i - (2 - i)$

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

$3 + 15 i - 4 i - 20 (i^{1} i) - (2 - i)$

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

$3 + 15 i - 4 i - 20 (i^{1} i^{1}) - (2 - i)$

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

$3 + 15 i - 4 i - 20 i^{1 + 1} - (2 - i)$

Add $1$ and $1$ .

$3 + 15 i - 4 i - 20 i^{2} - (2 - i)$

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

$3 + 15 i - 4 i - 20 \cdot - 1 - (2 - i)$

Multiply $- 20$ by $- 1$ .

$3 + 15 i - 4 i + 20 - (2 - i)$

Add $3$ and $20$ .

$23 + 15 i - 4 i - (2 - i)$

Subtract $4 i$ from $15 i$ .

$23 + 11 i - (2 - i)$

Apply the distributive property.

$23 + 11 i - 1 \cdot 2 - - i$

Multiply $- 1$ by $2$ .

$23 + 11 i - 2 - - i$

Multiply $- 1$ by $- 1$ .

$23 + 11 i - 2 + 1 i$

Multiply $i$ by $1$ .

$23 + 11 i - 2 + i$

Simplify by adding terms.

Subtract $2$ from $23$ .

$21 + 11 i + i$

Add $11 i$ and $i$ .

$21 + 12 i$

Simplify (3-4i)(1+5i)-(2-i)

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