Simplify 8(5-3i)+i(3+2i)

$8 (5 - 3 i) + i (3 + 2 i)$

Step 1

Simplify each term.

Apply the distributive property.

$8 \cdot 5 + 8 (- 3 i) + i (3 + 2 i)$

Multiply $8$ by $5$ .

$40 + 8 (- 3 i) + i (3 + 2 i)$

Multiply $- 3$ by $8$ .

$40 - 24 i + i (3 + 2 i)$

Apply the distributive property.

$40 - 24 i + i \cdot 3 + i (2 i)$

Move $3$ to the left of $i$ .

$40 - 24 i + 3 \cdot i + i (2 i)$

Multiply $i (2 i)$ .

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

$40 - 24 i + 3 \cdot i + 2 (i^{1} i)$

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

$40 - 24 i + 3 \cdot i + 2 (i^{1} i^{1})$

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

$40 - 24 i + 3 \cdot i + 2 i^{1 + 1}$

Add $1$ and $1$ .

$40 - 24 i + 3 \cdot i + 2 i^{2}$

$40 - 24 i + 3 \cdot i + 2 i^{2}$

Simplify each term.

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

$40 - 24 i + 3 i + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$40 - 24 i + 3 i - 2$

$40 - 24 i + 3 i - 2$

$40 - 24 i + 3 i - 2$

Step 2

Simplify by adding terms.

Subtract $2$ from $40$ .

$38 - 24 i + 3 i$

Add $- 24 i$ and $3 i$ .

$38 - 21 i$

$38 - 21 i$

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