Precalculus Examples

$- 4 + y i = x + 3 i$

Step 1

Add $4$ to both sides of the equation.

$y i = x + 3 i + 4$

Step 2

Divide each term in $y i = x + 3 i + 4$ by $i$ and simplify.

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Step 2.1

Divide each term in $y i = x + 3 i + 4$ by $i$ .

$\frac{y i}{i} = \frac{x}{i} + \frac{3 i}{i} + \frac{4}{i}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $i$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{y i}{i} = \frac{x}{i} + \frac{3 i}{i} + \frac{4}{i}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{x}{i} + \frac{3 i}{i} + \frac{4}{i}$

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

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

$y = \frac{x}{i} \cdot \frac{i}{i} + \frac{3 i}{i} + \frac{4}{i}$

Step 2.3.1.2

Multiply.

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Step 2.3.1.2.1

Combine.

$y = \frac{x i}{i i} + \frac{3 i}{i} + \frac{4}{i}$

Step 2.3.1.2.2

Simplify the denominator.

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Step 2.3.1.2.2.1

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

$y = \frac{x i}{i^{1} i} + \frac{3 i}{i} + \frac{4}{i}$

Step 2.3.1.2.2.2

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

$y = \frac{x i}{i^{1} i^{1}} + \frac{3 i}{i} + \frac{4}{i}$

Step 2.3.1.2.2.3

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

$y = \frac{x i}{i^{1 + 1}} + \frac{3 i}{i} + \frac{4}{i}$

Step 2.3.1.2.2.4

Add $1$ and $1$ .

$y = \frac{x i}{i^{2}} + \frac{3 i}{i} + \frac{4}{i}$

Step 2.3.1.2.2.5

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

$y = \frac{x i}{- 1} + \frac{3 i}{i} + \frac{4}{i}$

Step 2.3.1.3

Move the negative one from the denominator of $\frac{x i}{- 1}$ .

$y = - 1 \cdot (x i) + \frac{3 i}{i} + \frac{4}{i}$

Step 2.3.1.4

Rewrite $- 1 \cdot (x i)$ as $- (x i)$ .

$y = - (x i) + \frac{3 i}{i} + \frac{4}{i}$

Step 2.3.1.5

Cancel the common factor of $i$ .

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Step 2.3.1.5.1

Cancel the common factor.

$y = - x i + \frac{3 i}{i} + \frac{4}{i}$

Step 2.3.1.5.2

Divide $3$ by $1$ .

$y = - x i + 3 + \frac{4}{i}$

Step 2.3.1.6

Multiply the numerator and denominator of $\frac{4}{i}$ by the conjugate of $i$ to make the denominator real.

$y = - x i + 3 + \frac{4}{i} \cdot \frac{i}{i}$

Step 2.3.1.7

Multiply.

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Step 2.3.1.7.1

Combine.

$y = - x i + 3 + \frac{4 i}{i i}$

Step 2.3.1.7.2

Simplify the denominator.

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Step 2.3.1.7.2.1

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

$y = - x i + 3 + \frac{4 i}{i^{1} i}$

Step 2.3.1.7.2.2

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

$y = - x i + 3 + \frac{4 i}{i^{1} i^{1}}$

Step 2.3.1.7.2.3

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

$y = - x i + 3 + \frac{4 i}{i^{1 + 1}}$

Step 2.3.1.7.2.4

Add $1$ and $1$ .

$y = - x i + 3 + \frac{4 i}{i^{2}}$

Step 2.3.1.7.2.5

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

$y = - x i + 3 + \frac{4 i}{- 1}$

Step 2.3.1.8

Move the negative one from the denominator of $\frac{4 i}{- 1}$ .

$y = - x i + 3 - 1 \cdot (4 i)$

Step 2.3.1.9

Rewrite $- 1 \cdot (4 i)$ as $- (4 i)$ .

$y = - x i + 3 - (4 i)$

Step 2.3.1.10

Multiply $4$ by $- 1$ .

$y = - x i + 3 - 4 i$