Basic Math Examples

$\frac{- 38 - 3 i - 8 i^{2}}{10 - 4 i}$

Step 1

Multiply the numerator and denominator of $\frac{- 38 - 3 i - 8 i^{2}}{10 - 4 i}$ by the conjugate of $10 - 4 i$ to make the denominator real.

$\frac{- 38 - 3 i - 8 i^{2}}{10 - 4 i} \cdot \frac{10 + 4 i}{10 + 4 i}$

Step 2

Multiply.

Tap for more steps...

Step 2.1

Combine.

$\frac{(- 38 - 3 i - 8 i^{2}) (10 + 4 i)}{(10 - 4 i) (10 + 4 i)}$

Step 2.2

Simplify the numerator.

Tap for more steps...

Step 2.2.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1

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

$\frac{(- 38 - 3 i - 8 \cdot - 1) (10 + 4 i)}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.1.2

Multiply $- 8$ by $- 1$ .

$\frac{(- 38 - 3 i + 8) (10 + 4 i)}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.2

Add $- 38$ and $8$ .

$\frac{(- 30 - 3 i) (10 + 4 i)}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.3

Expand $(- 30 - 3 i) (10 + 4 i)$ using the FOIL Method.

Tap for more steps...

Step 2.2.3.1

Apply the distributive property.

$\frac{- 30 (10 + 4 i) - 3 i (10 + 4 i)}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.3.2

Apply the distributive property.

$\frac{- 30 \cdot 10 - 30 (4 i) - 3 i (10 + 4 i)}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.3.3

Apply the distributive property.

$\frac{- 30 \cdot 10 - 30 (4 i) - 3 i \cdot 10 - 3 i (4 i)}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.4

Simplify and combine like terms.

Tap for more steps...

Step 2.2.4.1

Simplify each term.

Tap for more steps...

Step 2.2.4.1.1

Multiply $- 30$ by $10$ .

$\frac{- 300 - 30 (4 i) - 3 i \cdot 10 - 3 i (4 i)}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.4.1.2

Multiply $4$ by $- 30$ .

$\frac{- 300 - 120 i - 3 i \cdot 10 - 3 i (4 i)}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.4.1.3

Multiply $10$ by $- 3$ .

$\frac{- 300 - 120 i - 30 i - 3 i (4 i)}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.4.1.4

Multiply $- 3 i (4 i)$ .

Tap for more steps...

Step 2.2.4.1.4.1

Multiply $4$ by $- 3$ .

$\frac{- 300 - 120 i - 30 i - 12 i i}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.4.1.4.2

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

$\frac{- 300 - 120 i - 30 i - 12 (i^{1} i)}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.4.1.4.3

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

$\frac{- 300 - 120 i - 30 i - 12 (i^{1} i^{1})}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.4.1.4.4

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

$\frac{- 300 - 120 i - 30 i - 12 i^{1 + 1}}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.4.1.4.5

Add $1$ and $1$ .

$\frac{- 300 - 120 i - 30 i - 12 i^{2}}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.4.1.5

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

$\frac{- 300 - 120 i - 30 i - 12 \cdot - 1}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.4.1.6

Multiply $- 12$ by $- 1$ .

$\frac{- 300 - 120 i - 30 i + 12}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.4.2

Add $- 300$ and $12$ .

$\frac{- 288 - 120 i - 30 i}{(10 - 4 i) (10 + 4 i)}$

Step 2.2.4.3

Subtract $30 i$ from $- 120 i$ .

$\frac{- 288 - 150 i}{(10 - 4 i) (10 + 4 i)}$

Step 2.3

Simplify the denominator.

Tap for more steps...

Step 2.3.1

Expand $(10 - 4 i) (10 + 4 i)$ using the FOIL Method.

Tap for more steps...

Step 2.3.1.1

Apply the distributive property.

$\frac{- 288 - 150 i}{10 (10 + 4 i) - 4 i (10 + 4 i)}$

Step 2.3.1.2

Apply the distributive property.

$\frac{- 288 - 150 i}{10 \cdot 10 + 10 (4 i) - 4 i (10 + 4 i)}$

Step 2.3.1.3

Apply the distributive property.

$\frac{- 288 - 150 i}{10 \cdot 10 + 10 (4 i) - 4 i \cdot 10 - 4 i (4 i)}$

Step 2.3.2

Simplify.

Tap for more steps...

Step 2.3.2.1

Multiply $10$ by $10$ .

$\frac{- 288 - 150 i}{100 + 10 (4 i) - 4 i \cdot 10 - 4 i (4 i)}$

Step 2.3.2.2

Multiply $4$ by $10$ .

$\frac{- 288 - 150 i}{100 + 40 i - 4 i \cdot 10 - 4 i (4 i)}$

Step 2.3.2.3

Multiply $10$ by $- 4$ .

$\frac{- 288 - 150 i}{100 + 40 i - 40 i - 4 i (4 i)}$

Step 2.3.2.4

Multiply $4$ by $- 4$ .

$\frac{- 288 - 150 i}{100 + 40 i - 40 i - 16 i i}$

Step 2.3.2.5

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

$\frac{- 288 - 150 i}{100 + 40 i - 40 i - 16 (i^{1} i)}$

Step 2.3.2.6

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

$\frac{- 288 - 150 i}{100 + 40 i - 40 i - 16 (i^{1} i^{1})}$

Step 2.3.2.7

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

$\frac{- 288 - 150 i}{100 + 40 i - 40 i - 16 i^{1 + 1}}$

Step 2.3.2.8

Add $1$ and $1$ .

$\frac{- 288 - 150 i}{100 + 40 i - 40 i - 16 i^{2}}$

Step 2.3.2.9

Subtract $40 i$ from $40 i$ .

$\frac{- 288 - 150 i}{100 + 0 - 16 i^{2}}$

Step 2.3.2.10

Add $100$ and $0$ .

$\frac{- 288 - 150 i}{100 - 16 i^{2}}$

Step 2.3.3

Simplify each term.

Tap for more steps...

Step 2.3.3.1

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

$\frac{- 288 - 150 i}{100 - 16 \cdot - 1}$

Step 2.3.3.2

Multiply $- 16$ by $- 1$ .

$\frac{- 288 - 150 i}{100 + 16}$

Step 2.3.4

Add $100$ and $16$ .

$\frac{- 288 - 150 i}{116}$

Step 3

Cancel the common factor of $- 288 - 150 i$ and $116$ .

Tap for more steps...

Step 3.1

Factor $2$ out of $- 288$ .

$\frac{2 (- 144) - 150 i}{116}$

Step 3.2

Factor $2$ out of $- 150 i$ .

$\frac{2 (- 144) + 2 (- 75 i)}{116}$

Step 3.3

Factor $2$ out of $2 (- 144) + 2 (- 75 i)$ .

$\frac{2 (- 144 - 75 i)}{116}$

Step 3.4

Cancel the common factors.

Tap for more steps...

Step 3.4.1

Factor $2$ out of $116$ .

$\frac{2 (- 144 - 75 i)}{2 \cdot 58}$

Step 3.4.2

Cancel the common factor.

$\frac{2 (- 144 - 75 i)}{2 \cdot 58}$

Step 3.4.3

Rewrite the expression.

$\frac{- 144 - 75 i}{58}$

Step 4

Split the fraction $\frac{- 144 - 75 i}{58}$ into two fractions.

$\frac{- 144}{58} + \frac{- 75 i}{58}$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Cancel the common factor of $- 144$ and $58$ .

Tap for more steps...

Step 5.1.1

Factor $2$ out of $- 144$ .

$\frac{2 (- 72)}{58} + \frac{- 75 i}{58}$

Step 5.1.2

Cancel the common factors.

Tap for more steps...

Step 5.1.2.1

Factor $2$ out of $58$ .

$\frac{2 \cdot - 72}{2 \cdot 29} + \frac{- 75 i}{58}$

Step 5.1.2.2

Cancel the common factor.

$\frac{2 \cdot - 72}{2 \cdot 29} + \frac{- 75 i}{58}$

Step 5.1.2.3

Rewrite the expression.

$\frac{- 72}{29} + \frac{- 75 i}{58}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{72}{29} + \frac{- 75 i}{58}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{72}{29} - \frac{75 i}{58}$