Finite Math Examples

$2 i y + 2 - 4 i = 0$

Step 1

Move all terms not containing $y$ to the right side of the equation.

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Step 1.1

Subtract $2$ from both sides of the equation.

$2 i y - 4 i = - 2$

Step 1.2

Add $4 i$ to both sides of the equation.

$2 i y = - 2 + 4 i$

Step 2

Divide each term in $2 i y = - 2 + 4 i$ by $2 i$ and simplify.

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Step 2.1

Divide each term in $2 i y = - 2 + 4 i$ by $2 i$ .

$\frac{2 i y}{2 i} = \frac{- 2}{2 i} + \frac{4 i}{2 i}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 i y}{2 i} = \frac{- 2}{2 i} + \frac{4 i}{2 i}$

Step 2.2.1.2

Rewrite the expression.

$\frac{i y}{i} = \frac{- 2}{2 i} + \frac{4 i}{2 i}$

Step 2.2.2

Cancel the common factor of $i$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{i y}{i} = \frac{- 2}{2 i} + \frac{4 i}{2 i}$

Step 2.2.2.2

Divide $y$ by $1$ .

$y = \frac{- 2}{2 i} + \frac{4 i}{2 i}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $- 2$ and $2$ .

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Step 2.3.1.1.1

Factor $2$ out of $- 2$ .

$y = \frac{2 \cdot - 1}{2 i} + \frac{4 i}{2 i}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $2$ out of $2 i$ .

$y = \frac{2 \cdot - 1}{2 (i)} + \frac{4 i}{2 i}$

Step 2.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot - 1}{2 i} + \frac{4 i}{2 i}$

Step 2.3.1.1.2.3

Rewrite the expression.

$y = \frac{- 1}{i} + \frac{4 i}{2 i}$

Step 2.3.1.2

Multiply the numerator and denominator of $\frac{- 1}{i}$ by the conjugate of $i$ to make the denominator real.

$y = \frac{- 1}{i} \cdot \frac{i}{i} + \frac{4 i}{2 i}$

Step 2.3.1.3

Multiply.

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Step 2.3.1.3.1

Combine.

$y = \frac{- i}{i i} + \frac{4 i}{2 i}$

Step 2.3.1.3.2

Simplify the denominator.

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Step 2.3.1.3.2.1

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

$y = \frac{- i}{i^{1} i} + \frac{4 i}{2 i}$

Step 2.3.1.3.2.2

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

$y = \frac{- i}{i^{1} i^{1}} + \frac{4 i}{2 i}$

Step 2.3.1.3.2.3

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

$y = \frac{- i}{i^{1 + 1}} + \frac{4 i}{2 i}$

Step 2.3.1.3.2.4

Add $1$ and $1$ .

$y = \frac{- i}{i^{2}} + \frac{4 i}{2 i}$

Step 2.3.1.3.2.5

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

$y = \frac{- i}{- 1} + \frac{4 i}{2 i}$

Step 2.3.1.4

Dividing two negative values results in a positive value.

$y = \frac{i}{1} + \frac{4 i}{2 i}$

Step 2.3.1.5

Divide $i$ by $1$ .

$y = i + \frac{4 i}{2 i}$

Step 2.3.1.6

Cancel the common factor of $4$ and $2$ .

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Step 2.3.1.6.1

Factor $2$ out of $4 i$ .

$y = i + \frac{2 (2 i)}{2 i}$

Step 2.3.1.6.2

Cancel the common factor.

$y = i + \frac{2 (2 i)}{2 i}$

Step 2.3.1.6.3

Rewrite the expression.

$y = i + 2$

Step 2.3.2

Reorder $i$ and $2$ .

$y = 2 + i$