Solve x+1/z-1=2i

$$\frac { x + 1 } { z - 1 } = 2 i$$

Solve for z

$$z=-\frac{ix}{2}+\left(1-\frac{1}{2}i\right)$$

$$x\neq -1$$

Steps for Solving Linear Equation

Variable z cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by z-1.

$$x+1=2i\left(z-1\right)$$

Use the distributive property to multiply 2i by z-1.

$$x+1=2iz-2i$$

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

$$2iz-2i=x+1$$

Add 2i to both sides.

$$2iz=x+1+2i$$

The equation is in standard form.

$$2iz=x+\left(1+2i\right)$$

Divide both sides by 2i.

$$\frac{2iz}{2i}=\frac{x+\left(1+2i\right)}{2i}$$

Dividing by 2i undoes the multiplication by 2i.

$$z=\frac{x+\left(1+2i\right)}{2i}$$

Divide x+\left(1+2i\right) by 2i.

$$z=-\frac{ix}{2}+\left(1-\frac{1}{2}i\right)$$

Variable z cannot be equal to 1.

$$z=-\frac{ix}{2}+\left(1-\frac{1}{2}i\right)\text{, }z\neq 1$$

Solve for x

$$x=2iz+\left(-1-2i\right)$$

$$z\neq 1$$