Basic Math Examples

$19 x - \sqrt{17} i = \frac{- 19}{17} + 13 y i$

Step 1

Rewrite the equation as $\frac{- 19}{17} + 13 y i = 19 x - \sqrt{17} i$ .

$\frac{- 19}{17} + 13 y i = 19 x - \sqrt{17} i$

Step 2

Move the negative in front of the fraction.

$- \frac{19}{17} + 13 y i = 19 x - \sqrt{17} i$

Step 3

Add $\frac{19}{17}$ to both sides of the equation.

$13 y i = 19 x - \sqrt{17} i + \frac{19}{17}$

Step 4

Divide each term in $13 y i = 19 x - \sqrt{17} i + \frac{19}{17}$ by $13 i$ and simplify.

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Step 4.1

Divide each term in $13 y i = 19 x - \sqrt{17} i + \frac{19}{17}$ by $13 i$ .

$\frac{13 y i}{13 i} = \frac{19 x}{13 i} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $13$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{13 y i}{13 i} = \frac{19 x}{13 i} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.2.1.2

Rewrite the expression.

$\frac{y i}{i} = \frac{19 x}{13 i} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.2.2

Cancel the common factor of $i$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{y i}{i} = \frac{19 x}{13 i} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.2.2.2

Divide $y$ by $1$ .

$y = \frac{19 x}{13 i} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Multiply the numerator and denominator of $\frac{19 x}{13 i}$ by the conjugate of $13 i$ to make the denominator real.

$y = \frac{19 x}{13 i} \cdot \frac{i}{i} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.2

Multiply.

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Step 4.3.1.2.1

Combine.

$y = \frac{19 x i}{13 i i} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.2.2

Simplify the denominator.

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Step 4.3.1.2.2.1

Add parentheses.

$y = \frac{19 x i}{13 (i i)} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.2.2.2

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

$y = \frac{19 x i}{13 (i^{1} i)} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.2.2.3

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

$y = \frac{19 x i}{13 (i^{1} i^{1})} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.2.2.4

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

$y = \frac{19 x i}{13 i^{1 + 1}} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.2.2.5

Add $1$ and $1$ .

$y = \frac{19 x i}{13 i^{2}} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.2.2.6

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

$y = \frac{19 x i}{13 \cdot - 1} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.3

Multiply $13$ by $- 1$ .

$y = \frac{19 x i}{- 13} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.4

Move the negative in front of the fraction.

$y = - \frac{19 x i}{13} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.5

Cancel the common factor of $i$ .

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Step 4.3.1.5.1

Cancel the common factor.

$y = - \frac{19 x i}{13} + \frac{- \sqrt{17} i}{13 i} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.5.2

Rewrite the expression.

$y = - \frac{19 x i}{13} + \frac{- \sqrt{17}}{13} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.6

Move the negative in front of the fraction.

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{\frac{19}{17}}{13 i}$

Step 4.3.1.7

Multiply the numerator and denominator of $\frac{\frac{19}{17}}{13 i}$ by the conjugate of $13 i$ to make the denominator real.

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{\frac{19}{17}}{13 i} \cdot \frac{i}{i}$

Step 4.3.1.8

Multiply.

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Step 4.3.1.8.1

Combine.

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{\frac{19}{17} i}{13 i i}$

Step 4.3.1.8.2

Combine $\frac{19}{17}$ and $i$ .

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{\frac{19 i}{17}}{13 i i}$

Step 4.3.1.8.3

Simplify the denominator.

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Step 4.3.1.8.3.1

Add parentheses.

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{\frac{19 i}{17}}{13 (i i)}$

Step 4.3.1.8.3.2

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

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{\frac{19 i}{17}}{13 (i^{1} i)}$

Step 4.3.1.8.3.3

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

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{\frac{19 i}{17}}{13 (i^{1} i^{1})}$

Step 4.3.1.8.3.4

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

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{\frac{19 i}{17}}{13 i^{1 + 1}}$

Step 4.3.1.8.3.5

Add $1$ and $1$ .

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{\frac{19 i}{17}}{13 i^{2}}$

Step 4.3.1.8.3.6

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

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{\frac{19 i}{17}}{13 \cdot - 1}$

Step 4.3.1.9

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{19 i}{17} \cdot \frac{1}{13 \cdot - 1}$

Step 4.3.1.10

Cancel the common factor of $1$ and $- 1$ .

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Step 4.3.1.10.1

Rewrite $1$ as $- 1 (- 1)$ .

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{19 i}{17} \cdot \frac{- 1 (- 1)}{13 \cdot - 1}$

Step 4.3.1.10.2

Move the negative in front of the fraction.

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} + \frac{19 i}{17} (- \frac{1}{13})$

Step 4.3.1.11

Multiply $\frac{19 i}{17} (- \frac{1}{13})$ .

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Step 4.3.1.11.1

Multiply $\frac{19 i}{17}$ by $\frac{1}{13}$ .

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} - \frac{19 i}{17 \cdot 13}$

Step 4.3.1.11.2

Multiply $17$ by $13$ .

$y = - \frac{19 x i}{13} - \frac{\sqrt{17}}{13} - \frac{19 i}{221}$