Basic Math Examples

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

Step 1

Cancel the common factor of $2 + i$ .

Tap for more steps...

Step 1.1

Cancel the common factor.

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

Step 1.2

Rewrite the expression.

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

Step 2

Multiply $\frac{6 - 8 i}{2 - i}$ by $1$ .

$\frac{6 - 8 i}{2 - i}$

Step 3

Multiply the numerator and denominator of $\frac{6 - 8 i}{2 - i}$ by the conjugate of $2 - i$ to make the denominator real.

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

Step 4

Multiply.

Tap for more steps...

Step 4.1

Combine.

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

Step 4.2

Simplify the numerator.

Tap for more steps...

Step 4.2.1

Expand $(6 - 8 i) (2 + i)$ using the FOIL Method.

Tap for more steps...

Step 4.2.1.1

Apply the distributive property.

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

Step 4.2.1.2

Apply the distributive property.

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

Step 4.2.1.3

Apply the distributive property.

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

Step 4.2.2

Simplify and combine like terms.

Tap for more steps...

Step 4.2.2.1

Simplify each term.

Tap for more steps...

Step 4.2.2.1.1

Multiply $6$ by $2$ .

$\frac{12 + 6 i - 8 i \cdot 2 - 8 i i}{(2 - i) (2 + i)}$

Step 4.2.2.1.2

Multiply $2$ by $- 8$ .

$\frac{12 + 6 i - 16 i - 8 i i}{(2 - i) (2 + i)}$

Step 4.2.2.1.3

Multiply $- 8 i i$ .

Tap for more steps...

Step 4.2.2.1.3.1

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

$\frac{12 + 6 i - 16 i - 8 (i^{1} i)}{(2 - i) (2 + i)}$

Step 4.2.2.1.3.2

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

$\frac{12 + 6 i - 16 i - 8 (i^{1} i^{1})}{(2 - i) (2 + i)}$

Step 4.2.2.1.3.3

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

$\frac{12 + 6 i - 16 i - 8 i^{1 + 1}}{(2 - i) (2 + i)}$

Step 4.2.2.1.3.4

Add $1$ and $1$ .

$\frac{12 + 6 i - 16 i - 8 i^{2}}{(2 - i) (2 + i)}$

Step 4.2.2.1.4

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

$\frac{12 + 6 i - 16 i - 8 \cdot - 1}{(2 - i) (2 + i)}$

Step 4.2.2.1.5

Multiply $- 8$ by $- 1$ .

$\frac{12 + 6 i - 16 i + 8}{(2 - i) (2 + i)}$

Step 4.2.2.2

Add $12$ and $8$ .

$\frac{20 + 6 i - 16 i}{(2 - i) (2 + i)}$

Step 4.2.2.3

Subtract $16 i$ from $6 i$ .

$\frac{20 - 10 i}{(2 - i) (2 + i)}$

Step 4.3

Simplify the denominator.

Tap for more steps...

Step 4.3.1

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

Tap for more steps...

Step 4.3.1.1

Apply the distributive property.

$\frac{20 - 10 i}{2 (2 + i) - i (2 + i)}$

Step 4.3.1.2

Apply the distributive property.

$\frac{20 - 10 i}{2 \cdot 2 + 2 i - i (2 + i)}$

Step 4.3.1.3

Apply the distributive property.

$\frac{20 - 10 i}{2 \cdot 2 + 2 i - i \cdot 2 - i i}$

Step 4.3.2

Simplify.

Tap for more steps...

Step 4.3.2.1

Multiply $2$ by $2$ .

$\frac{20 - 10 i}{4 + 2 i - i \cdot 2 - i i}$

Step 4.3.2.2

Multiply $2$ by $- 1$ .

$\frac{20 - 10 i}{4 + 2 i - 2 i - i i}$

Step 4.3.2.3

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

$\frac{20 - 10 i}{4 + 2 i - 2 i - (i^{1} i)}$

Step 4.3.2.4

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

$\frac{20 - 10 i}{4 + 2 i - 2 i - (i^{1} i^{1})}$

Step 4.3.2.5

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

$\frac{20 - 10 i}{4 + 2 i - 2 i - i^{1 + 1}}$

Step 4.3.2.6

Add $1$ and $1$ .

$\frac{20 - 10 i}{4 + 2 i - 2 i - i^{2}}$

Step 4.3.2.7

Subtract $2 i$ from $2 i$ .

$\frac{20 - 10 i}{4 + 0 - i^{2}}$

Step 4.3.2.8

Add $4$ and $0$ .

$\frac{20 - 10 i}{4 - i^{2}}$

Step 4.3.3

Simplify each term.

Tap for more steps...

Step 4.3.3.1

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

$\frac{20 - 10 i}{4 - - 1}$

Step 4.3.3.2

Multiply $- 1$ by $- 1$ .

$\frac{20 - 10 i}{4 + 1}$

Step 4.3.4

Add $4$ and $1$ .

$\frac{20 - 10 i}{5}$

Step 5

Cancel the common factor of $20 - 10 i$ and $5$ .

Tap for more steps...

Step 5.1

Factor $5$ out of $20$ .

$\frac{5 \cdot 4 - 10 i}{5}$

Step 5.2

Factor $5$ out of $- 10 i$ .

$\frac{5 \cdot 4 + 5 (- 2 i)}{5}$

Step 5.3

Factor $5$ out of $5 (4) + 5 (- 2 i)$ .

$\frac{5 (4 - 2 i)}{5}$

Step 5.4

Cancel the common factors.

Tap for more steps...

Step 5.4.1

Factor $5$ out of $5$ .

$\frac{5 (4 - 2 i)}{5 (1)}$

Step 5.4.2

Cancel the common factor.

$\frac{5 (4 - 2 i)}{5 \cdot 1}$

Step 5.4.3

Rewrite the expression.

$\frac{4 - 2 i}{1}$

Step 5.4.4

Divide $4 - 2 i$ by $1$ .

$4 - 2 i$