Solve for y 4x+2i=8+yi

$4 x + 2 i = 8 + y i$

Rewrite the equation as $8 + y i = 4 x + 2 i$ .

$8 + y i = 4 x + 2 i$

Subtract $8$ from both sides of the equation.

$y i = 4 x + 2 i - 8$

Divide each term in $y i = 4 x + 2 i - 8$ by $i$ and simplify.

Divide each term in $y i = 4 x + 2 i - 8$ by $i$ .

$\frac{y i}{i} = \frac{4 x}{i} + \frac{2 i}{i} + \frac{- 8}{i}$

Simplify the left side.

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{y i}{i} = \frac{4 x}{i} + \frac{2 i}{i} + \frac{- 8}{i}$

Divide $y$ by $1$ .

$y = \frac{4 x}{i} + \frac{2 i}{i} + \frac{- 8}{i}$

Simplify the right side.

Simplify each term.

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

$y = \frac{4 x}{i} \cdot \frac{i}{i} + \frac{2 i}{i} + \frac{- 8}{i}$

Multiply.

Combine.

$y = \frac{4 x i}{i i} + \frac{2 i}{i} + \frac{- 8}{i}$

Simplify the denominator.

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

$y = \frac{4 x i}{i^{1} i} + \frac{2 i}{i} + \frac{- 8}{i}$

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

$y = \frac{4 x i}{i^{1} i^{1}} + \frac{2 i}{i} + \frac{- 8}{i}$

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

$y = \frac{4 x i}{i^{1 + 1}} + \frac{2 i}{i} + \frac{- 8}{i}$

Add $1$ and $1$ .

$y = \frac{4 x i}{i^{2}} + \frac{2 i}{i} + \frac{- 8}{i}$

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

$y = \frac{4 x i}{- 1} + \frac{2 i}{i} + \frac{- 8}{i}$

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

$y = - 1 \cdot (4 x i) + \frac{2 i}{i} + \frac{- 8}{i}$

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

$y = - (4 x i) + \frac{2 i}{i} + \frac{- 8}{i}$

Multiply $4$ by $- 1$ .

$y = - 4 (x i) + \frac{2 i}{i} + \frac{- 8}{i}$

Cancel the common factor of $i$ .

Cancel the common factor.

$y = - 4 x i + \frac{2 i}{i} + \frac{- 8}{i}$

Divide $2$ by $1$ .

$y = - 4 x i + 2 + \frac{- 8}{i}$

Multiply the numerator and denominator of $\frac{- 8}{i}$ by the conjugate of $i$ to make the denominator real.

$y = - 4 x i + 2 + \frac{- 8}{i} \cdot \frac{i}{i}$

Multiply.

Combine.

$y = - 4 x i + 2 + \frac{- 8 i}{i i}$

Simplify the denominator.

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

$y = - 4 x i + 2 + \frac{- 8 i}{i^{1} i}$

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

$y = - 4 x i + 2 + \frac{- 8 i}{i^{1} i^{1}}$

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

$y = - 4 x i + 2 + \frac{- 8 i}{i^{1 + 1}}$

Add $1$ and $1$ .

$y = - 4 x i + 2 + \frac{- 8 i}{i^{2}}$

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

$y = - 4 x i + 2 + \frac{- 8 i}{- 1}$

Move the negative one from the denominator of $\frac{- 8 i}{- 1}$ .

$y = - 4 x i + 2 - 1 \cdot (- 8 i)$

Rewrite $- 1 \cdot (- 8 i)$ as $- (- 8 i)$ .

$y = - 4 x i + 2 - (- 8 i)$

Multiply $- 8$ by $- 1$ .

$y = - 4 x i + 2 + 8 i$

Solve for y 4x+2i=8+yi

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