Evaluate 4x+2i=8+yi

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

Subtract $2 i$ from both sides of the equation.

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

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $8$ by $4$ .

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

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

Factor $2$ out of $- 2 i$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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