Solve for y -12x+yi=60-13i

$- 12 x + y i = 60 - 13 i$

Add $12 x$ to both sides of the equation.

$y i = 60 - 13 i + 12 x$

Divide each term in $y i = 60 - 13 i + 12 x$ by $i$ and simplify.

Divide each term in $y i = 60 - 13 i + 12 x$ by $i$ .

$\frac{y i}{i} = \frac{60}{i} + \frac{- 13 i}{i} + \frac{12 x}{i}$

Simplify the left side.

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{y i}{i} = \frac{60}{i} + \frac{- 13 i}{i} + \frac{12 x}{i}$

Divide $y$ by $1$ .

$y = \frac{60}{i} + \frac{- 13 i}{i} + \frac{12 x}{i}$

Simplify the right side.

Simplify each term.

Multiply the numerator and denominator of $\frac{60}{i}$ by the conjugate of $i$ to make the denominator real.

$y = \frac{60}{i} \cdot \frac{i}{i} + \frac{- 13 i}{i} + \frac{12 x}{i}$

Multiply.

Combine.

$y = \frac{60 i}{i i} + \frac{- 13 i}{i} + \frac{12 x}{i}$

Simplify the denominator.

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

$y = \frac{60 i}{i^{1} i} + \frac{- 13 i}{i} + \frac{12 x}{i}$

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

$y = \frac{60 i}{i^{1} i^{1}} + \frac{- 13 i}{i} + \frac{12 x}{i}$

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

$y = \frac{60 i}{i^{1 + 1}} + \frac{- 13 i}{i} + \frac{12 x}{i}$

Add $1$ and $1$ .

$y = \frac{60 i}{i^{2}} + \frac{- 13 i}{i} + \frac{12 x}{i}$

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

$y = \frac{60 i}{- 1} + \frac{- 13 i}{i} + \frac{12 x}{i}$

Move the negative one from the denominator of $\frac{60 i}{- 1}$ .

$y = - 1 \cdot (60 i) + \frac{- 13 i}{i} + \frac{12 x}{i}$

Rewrite $- 1 \cdot (60 i)$ as $- (60 i)$ .

$y = - (60 i) + \frac{- 13 i}{i} + \frac{12 x}{i}$

Multiply $60$ by $- 1$ .

$y = - 60 i + \frac{- 13 i}{i} + \frac{12 x}{i}$

Cancel the common factor of $i$ .

Cancel the common factor.

$y = - 60 i + \frac{- 13 i}{i} + \frac{12 x}{i}$

Divide $- 13$ by $1$ .

$y = - 60 i - 13 + \frac{12 x}{i}$

Multiply the numerator and denominator of $\frac{12 x}{i}$ by the conjugate of $i$ to make the denominator real.

$y = - 60 i - 13 + \frac{12 x}{i} \cdot \frac{i}{i}$

Multiply.

Combine.

$y = - 60 i - 13 + \frac{12 x i}{i i}$

Simplify the denominator.

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

$y = - 60 i - 13 + \frac{12 x i}{i^{1} i}$

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

$y = - 60 i - 13 + \frac{12 x i}{i^{1} i^{1}}$

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

$y = - 60 i - 13 + \frac{12 x i}{i^{1 + 1}}$

Add $1$ and $1$ .

$y = - 60 i - 13 + \frac{12 x i}{i^{2}}$

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

$y = - 60 i - 13 + \frac{12 x i}{- 1}$

Move the negative one from the denominator of $\frac{12 x i}{- 1}$ .

$y = - 60 i - 13 - 1 \cdot (12 x i)$

Rewrite $- 1 \cdot (12 x i)$ as $- (12 x i)$ .

$y = - 60 i - 13 - (12 x i)$

Multiply $12$ by $- 1$ .

$y = - 60 i - 13 - 12 x i$

Reorder $- 60 i$ and $- 13$ .

$y = - 13 - 60 i - 12 x i$

Solve for y -12x+yi=60-13i

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