Simplify (2+i)(8-3i)-(23+34i)

$(2 + i) (8 - 3 i) - (23 + 34 i)$

Step 1

Simplify each term.

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

Apply the distributive property.

$2 (8 - 3 i) + i (8 - 3 i) - (23 + 34 i)$

Apply the distributive property.

$2 \cdot 8 + 2 (- 3 i) + i (8 - 3 i) - (23 + 34 i)$

Apply the distributive property.

$2 \cdot 8 + 2 (- 3 i) + i \cdot 8 + i (- 3 i) - (23 + 34 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $8$ .

$16 + 2 (- 3 i) + i \cdot 8 + i (- 3 i) - (23 + 34 i)$

Multiply $- 3$ by $2$ .

$16 - 6 i + i \cdot 8 + i (- 3 i) - (23 + 34 i)$

Move $8$ to the left of $i$ .

$16 - 6 i + 8 \cdot i + i (- 3 i) - (23 + 34 i)$

Multiply $i (- 3 i)$ .

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

$16 - 6 i + 8 i - 3 (i^{1} i) - (23 + 34 i)$

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

$16 - 6 i + 8 i - 3 (i^{1} i^{1}) - (23 + 34 i)$

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

$16 - 6 i + 8 i - 3 i^{1 + 1} - (23 + 34 i)$

Add $1$ and $1$ .

$16 - 6 i + 8 i - 3 i^{2} - (23 + 34 i)$

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

$16 - 6 i + 8 i - 3 \cdot - 1 - (23 + 34 i)$

Multiply $- 3$ by $- 1$ .

$16 - 6 i + 8 i + 3 - (23 + 34 i)$

Add $16$ and $3$ .

$19 - 6 i + 8 i - (23 + 34 i)$

Add $- 6 i$ and $8 i$ .

$19 + 2 i - (23 + 34 i)$

Apply the distributive property.

$19 + 2 i - 1 \cdot 23 - (34 i)$

Multiply $- 1$ by $23$ .

$19 + 2 i - 23 - (34 i)$

Multiply $34$ by $- 1$ .

$19 + 2 i - 23 - 34 i$

Step 2

Simplify by adding terms.

Subtract $23$ from $19$ .

$- 4 + 2 i - 34 i$

Subtract $34 i$ from $2 i$ .

$- 4 - 32 i$

Simplify (2+i)(8-3i)-(23+34i)

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