Simplify (1/2+i)(8-6i)

$(\frac{1}{2} + i) (8 - 6 i)$

Step 1

Expand $(\frac{1}{2} + i) (8 - 6 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{1}{2} (8 - 6 i) + i (8 - 6 i)$

Apply the distributive property.

$\frac{1}{2} \cdot 8 + \frac{1}{2} (- 6 i) + i (8 - 6 i)$

Apply the distributive property.

$\frac{1}{2} \cdot 8 + \frac{1}{2} (- 6 i) + i \cdot 8 + i (- 6 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{1}{2} \cdot (2 (4)) + \frac{1}{2} (- 6 i) + i \cdot 8 + i (- 6 i)$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 4) + \frac{1}{2} (- 6 i) + i \cdot 8 + i (- 6 i)$

Rewrite the expression.

$4 + \frac{1}{2} (- 6 i) + i \cdot 8 + i (- 6 i)$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6 i$ .

$4 + \frac{1}{2} (2 (- 3 i)) + i \cdot 8 + i (- 6 i)$

Cancel the common factor.

$4 + \frac{1}{2} (2 (- 3 i)) + i \cdot 8 + i (- 6 i)$

Rewrite the expression.

$4 - 3 i + i \cdot 8 + i (- 6 i)$

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

$4 - 3 i + 8 \cdot i + i (- 6 i)$

Multiply $i (- 6 i)$ .

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

$4 - 3 i + 8 i - 6 (i^{1} i)$

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

$4 - 3 i + 8 i - 6 (i^{1} i^{1})$

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

$4 - 3 i + 8 i - 6 i^{1 + 1}$

Add $1$ and $1$ .

$4 - 3 i + 8 i - 6 i^{2}$

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

$4 - 3 i + 8 i - 6 \cdot - 1$

Multiply $- 6$ by $- 1$ .

$4 - 3 i + 8 i + 6$

Add $4$ and $6$ .

$10 - 3 i + 8 i$

Add $- 3 i$ and $8 i$ .

$10 + 5 i$