Solve 2z-1/z+i=i

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

Solve for z

$$z=0$$

Steps for Solving Linear Equation

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

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

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

$$2z-1=iz-1$$

Subtract iz from both sides.

$$2z-1-iz=-1$$

Combine 2z and -iz to get \left(2-i\right)z.

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

Add 1 to both sides.

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

Add -1 and 1 to get 0.

$$\left(2-i\right)z=0$$

Divide both sides by 2-i. Zero divided by any non-zero number gives zero.

$$z=0$$