Solve 8i=(x+2i)(y+2i)+1

$$8 i = ( x + 2 i ) ( y + 2 i ) + 1$$

Solve for x

$$x=-\frac{2iy+\left(-3-8i\right)}{y+2i}$$

$$y\neq -2i$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+2i by y+2i.

$$8i=xy+2ix+2iy-4+1$$

Add -4 and 1 to get -3.

$$8i=xy+2ix+2iy-3$$

Swap sides so that all variable terms are on the left hand side.

$$xy+2ix+2iy-3=8i$$

Subtract 2iy from both sides.

$$xy+2ix-3=8i-2iy$$

Add 3 to both sides.

$$xy+2ix=8i-2iy+3$$

Combine all terms containing x.

$$\left(y+2i\right)x=8i-2iy+3$$

The equation is in standard form.

$$\left(y+2i\right)x=3+8i-2iy$$

Divide both sides by y+2i.

$$\frac{\left(y+2i\right)x}{y+2i}=\frac{3+8i-2iy}{y+2i}$$

Dividing by y+2i undoes the multiplication by y+2i.

$$x=\frac{3+8i-2iy}{y+2i}$$

Solve for y

$$y=-\frac{2ix+\left(-3-8i\right)}{x+2i}$$

$$x\neq -2i$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+2i by y+2i.

$$8i=xy+2ix+2iy-4+1$$

Add -4 and 1 to get -3.

$$8i=xy+2ix+2iy-3$$

Swap sides so that all variable terms are on the left hand side.

$$xy+2ix+2iy-3=8i$$

Subtract 2ix from both sides.

$$xy+2iy-3=8i-2ix$$

Add 3 to both sides.

$$xy+2iy=8i-2ix+3$$

Combine all terms containing y.

$$\left(x+2i\right)y=8i-2ix+3$$

The equation is in standard form.

$$\left(x+2i\right)y=3+8i-2ix$$

Divide both sides by x+2i.

$$\frac{\left(x+2i\right)y}{x+2i}=\frac{3+8i-2ix}{x+2i}$$

Dividing by x+2i undoes the multiplication by x+2i.

$$y=\frac{3+8i-2ix}{x+2i}$$