Solve 1+z/1-z=-i

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

Solve for z

$$z=-i$$

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.

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

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

$$1+z=iz-i$$

Subtract iz from both sides.

$$1+z-iz=-i$$

Combine z and -iz to get \left(1-i\right)z.

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

Subtract 1 from both sides.

$$\left(1-i\right)z=-i-1$$

The equation is in standard form.

$$\left(1-i\right)z=-1-i$$

Divide both sides by 1-i.

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

Dividing by 1-i undoes the multiplication by 1-i.

$$z=\frac{-1-i}{1-i}$$

Divide -1-i by 1-i.

$$z=-i$$