Solve for y 9+12i=3x+4yi

$9 + 12 i = 3 x + 4 y i$

Rewrite the equation as $3 x + 4 y i = 9 + 12 i$ .

$3 x + 4 y i = 9 + 12 i$

Subtract $3 x$ from both sides of the equation.

$4 y i = 9 + 12 i - 3 x$

Divide each term in $4 y i = 9 + 12 i - 3 x$ by $4 i$ and simplify.

Divide each term in $4 y i = 9 + 12 i - 3 x$ by $4 i$ .

$\frac{4 y i}{4 i} = \frac{9}{4 i} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y i}{4 i} = \frac{9}{4 i} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

Rewrite the expression.

$\frac{y i}{i} = \frac{9}{4 i} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{y i}{i} = \frac{9}{4 i} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

Divide $y$ by $1$ .

$y = \frac{9}{4 i} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

Simplify the right side.

Simplify each term.

Multiply the numerator and denominator of $\frac{9}{4 i}$ by the conjugate of $4 i$ to make the denominator real.

$y = \frac{9}{4 i} \cdot \frac{i}{i} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

Multiply.

Combine.

$y = \frac{9 i}{4 i i} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

Simplify the denominator.

Add parentheses.

$y = \frac{9 i}{4 (i i)} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

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

$y = \frac{9 i}{4 (i^{1} i)} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

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

$y = \frac{9 i}{4 (i^{1} i^{1})} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

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

$y = \frac{9 i}{4 i^{1 + 1}} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

Add $1$ and $1$ .

$y = \frac{9 i}{4 i^{2}} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

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

$y = \frac{9 i}{4 \cdot - 1} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

Multiply $4$ by $- 1$ .

$y = \frac{9 i}{- 4} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

Move the negative in front of the fraction.

$y = - \frac{9 i}{4} + \frac{12 i}{4 i} + \frac{- 3 x}{4 i}$

Cancel the common factor of $12$ and $4$ .

Factor $4$ out of $12 i$ .

$y = - \frac{9 i}{4} + \frac{4 (3 i)}{4 i} + \frac{- 3 x}{4 i}$

Cancel the common factors.

Factor $4$ out of $4 i$ .

$y = - \frac{9 i}{4} + \frac{4 (3 i)}{4 (i)} + \frac{- 3 x}{4 i}$

Cancel the common factor.

$y = - \frac{9 i}{4} + \frac{4 (3 i)}{4 i} + \frac{- 3 x}{4 i}$

Rewrite the expression.

$y = - \frac{9 i}{4} + \frac{3 i}{i} + \frac{- 3 x}{4 i}$

Cancel the common factor of $i$ .

Cancel the common factor.

$y = - \frac{9 i}{4} + \frac{3 i}{i} + \frac{- 3 x}{4 i}$

Divide $3$ by $1$ .

$y = - \frac{9 i}{4} + 3 + \frac{- 3 x}{4 i}$

Multiply the numerator and denominator of $\frac{- 3 x}{4 i}$ by the conjugate of $4 i$ to make the denominator real.

$y = - \frac{9 i}{4} + 3 + \frac{- 3 x}{4 i} \cdot \frac{i}{i}$

Multiply.

Combine.

$y = - \frac{9 i}{4} + 3 + \frac{- 3 x i}{4 i i}$

Simplify the denominator.

Add parentheses.

$y = - \frac{9 i}{4} + 3 + \frac{- 3 x i}{4 (i i)}$

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

$y = - \frac{9 i}{4} + 3 + \frac{- 3 x i}{4 (i^{1} i)}$

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

$y = - \frac{9 i}{4} + 3 + \frac{- 3 x i}{4 (i^{1} i^{1})}$

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

$y = - \frac{9 i}{4} + 3 + \frac{- 3 x i}{4 i^{1 + 1}}$

Add $1$ and $1$ .

$y = - \frac{9 i}{4} + 3 + \frac{- 3 x i}{4 i^{2}}$

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

$y = - \frac{9 i}{4} + 3 + \frac{- 3 x i}{4 \cdot - 1}$

Multiply $4$ by $- 1$ .

$y = - \frac{9 i}{4} + 3 + \frac{- 3 x i}{- 4}$

Dividing two negative values results in a positive value.

$y = - \frac{9 i}{4} + 3 + \frac{3 x i}{4}$

Reorder $- \frac{9 i}{4}$ and $3$ .

$y = 3 - \frac{9 i}{4} + \frac{3 x i}{4}$

Solve for y 9+12i=3x+4yi

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