Solve for x (5+4i)-(x+yi)=-1-3i

$(5 + 4 i) - (x + y i) = - 1 - 3 i$

Step 1

Simplify each term.

$5 + 4 i - x - y i = - 1 - 3 i$

Step 2

Move all terms not containing $x$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$4 i - x - y i = - 1 - 3 i - 5$

Subtract $4 i$ from both sides of the equation.

$- x - y i = - 1 - 3 i - 5 - 4 i$

Add $y i$ to both sides of the equation.

$- x = - 1 - 3 i - 5 - 4 i + y i$

Subtract $5$ from $- 1$ .

$- x = - 6 - 3 i - 4 i + y i$

Subtract $4 i$ from $- 3 i$ .

$- x = - 6 - 7 i + y i$

Step 3

Divide each term in $- x = - 6 - 7 i + y i$ by $- 1$ and simplify.

Divide each term in $- x = - 6 - 7 i + y i$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 6}{- 1} + \frac{- 7 i}{- 1} + \frac{y i}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 6}{- 1} + \frac{- 7 i}{- 1} + \frac{y i}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 1} + \frac{- 7 i}{- 1} + \frac{y i}{- 1}$

Simplify the right side.

Simplify each term.

Divide $- 6$ by $- 1$ .

$x = 6 + \frac{- 7 i}{- 1} + \frac{y i}{- 1}$

Move the negative one from the denominator of $\frac{- 7 i}{- 1}$ .

$x = 6 - 1 \cdot (- 7 i) + \frac{y i}{- 1}$

Rewrite $- 1 \cdot (- 7 i)$ as $- (- 7 i)$ .

$x = 6 - (- 7 i) + \frac{y i}{- 1}$

Multiply $- 7$ by $- 1$ .

$x = 6 + 7 i + \frac{y i}{- 1}$

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

$x = 6 + 7 i - 1 \cdot (y i)$

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

$x = 6 + 7 i - y i$