Trigonometry Examples

$32 + 5 y i = 16 x - 40 i$

Step 1

Subtract $32$ from both sides of the equation.

$5 y i = 16 x - 40 i - 32$

Step 2

Divide each term in $5 y i = 16 x - 40 i - 32$ by $5 i$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $5 y i = 16 x - 40 i - 32$ by $5 i$ .

$\frac{5 y i}{5 i} = \frac{16 x}{5 i} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{5 y i}{5 i} = \frac{16 x}{5 i} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.2.1.2

Rewrite the expression.

$\frac{y i}{i} = \frac{16 x}{5 i} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.2.2

Cancel the common factor of $i$ .

Tap for more steps...

Step 2.2.2.1

Cancel the common factor.

$\frac{y i}{i} = \frac{16 x}{5 i} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.2.2.2

Divide $y$ by $1$ .

$y = \frac{16 x}{5 i} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Simplify each term.

Tap for more steps...

Step 2.3.1.1

Multiply the numerator and denominator of $\frac{16 x}{5 i}$ by the conjugate of $5 i$ to make the denominator real.

$y = \frac{16 x}{5 i} \cdot \frac{i}{i} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.3.1.2

Multiply.

Tap for more steps...

Step 2.3.1.2.1

Combine.

$y = \frac{16 x i}{5 i i} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.3.1.2.2

Simplify the denominator.

Tap for more steps...

Step 2.3.1.2.2.1

Add parentheses.

$y = \frac{16 x i}{5 (i i)} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.3.1.2.2.2

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

$y = \frac{16 x i}{5 (i^{1} i)} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.3.1.2.2.3

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

$y = \frac{16 x i}{5 (i^{1} i^{1})} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.3.1.2.2.4

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

$y = \frac{16 x i}{5 i^{1 + 1}} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.3.1.2.2.5

Add $1$ and $1$ .

$y = \frac{16 x i}{5 i^{2}} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.3.1.2.2.6

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

$y = \frac{16 x i}{5 \cdot - 1} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.3.1.3

Multiply $5$ by $- 1$ .

$y = \frac{16 x i}{- 5} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.3.1.4

Move the negative in front of the fraction.

$y = - \frac{16 x i}{5} + \frac{- 40 i}{5 i} + \frac{- 32}{5 i}$

Step 2.3.1.5

Cancel the common factor of $- 40$ and $5$ .

Tap for more steps...

Step 2.3.1.5.1

Factor $5$ out of $- 40 i$ .

$y = - \frac{16 x i}{5} + \frac{5 (- 8 i)}{5 i} + \frac{- 32}{5 i}$

Step 2.3.1.5.2

Cancel the common factors.

Tap for more steps...

Step 2.3.1.5.2.1

Factor $5$ out of $5 i$ .

$y = - \frac{16 x i}{5} + \frac{5 (- 8 i)}{5 (i)} + \frac{- 32}{5 i}$

Step 2.3.1.5.2.2

Cancel the common factor.

$y = - \frac{16 x i}{5} + \frac{5 (- 8 i)}{5 i} + \frac{- 32}{5 i}$

Step 2.3.1.5.2.3

Rewrite the expression.

$y = - \frac{16 x i}{5} + \frac{- 8 i}{i} + \frac{- 32}{5 i}$

Step 2.3.1.6

Cancel the common factor of $i$ .

Tap for more steps...

Step 2.3.1.6.1

Cancel the common factor.

$y = - \frac{16 x i}{5} + \frac{- 8 i}{i} + \frac{- 32}{5 i}$

Step 2.3.1.6.2

Divide $- 8$ by $1$ .

$y = - \frac{16 x i}{5} - 8 + \frac{- 32}{5 i}$

Step 2.3.1.7

Multiply the numerator and denominator of $\frac{- 32}{5 i}$ by the conjugate of $5 i$ to make the denominator real.

$y = - \frac{16 x i}{5} - 8 + \frac{- 32}{5 i} \cdot \frac{i}{i}$

Step 2.3.1.8

Multiply.

Tap for more steps...

Step 2.3.1.8.1

Combine.

$y = - \frac{16 x i}{5} - 8 + \frac{- 32 i}{5 i i}$

Step 2.3.1.8.2

Simplify the denominator.

Tap for more steps...

Step 2.3.1.8.2.1

Add parentheses.

$y = - \frac{16 x i}{5} - 8 + \frac{- 32 i}{5 (i i)}$

Step 2.3.1.8.2.2

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

$y = - \frac{16 x i}{5} - 8 + \frac{- 32 i}{5 (i^{1} i)}$

Step 2.3.1.8.2.3

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

$y = - \frac{16 x i}{5} - 8 + \frac{- 32 i}{5 (i^{1} i^{1})}$

Step 2.3.1.8.2.4

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

$y = - \frac{16 x i}{5} - 8 + \frac{- 32 i}{5 i^{1 + 1}}$

Step 2.3.1.8.2.5

Add $1$ and $1$ .

$y = - \frac{16 x i}{5} - 8 + \frac{- 32 i}{5 i^{2}}$

Step 2.3.1.8.2.6

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

$y = - \frac{16 x i}{5} - 8 + \frac{- 32 i}{5 \cdot - 1}$

Step 2.3.1.9

Multiply $5$ by $- 1$ .

$y = - \frac{16 x i}{5} - 8 + \frac{- 32 i}{- 5}$

Step 2.3.1.10

Dividing two negative values results in a positive value.

$y = - \frac{16 x i}{5} - 8 + \frac{32 i}{5}$