Solve 12=z-2+1/z+2i

$$12 = \frac { z - 2 + 1 } { z + 2 i }$$

Solve for z

$$z=-\frac{1}{11}-\frac{24}{11}i\approx -0.090909091-2.181818182i$$

Steps for Solving Linear Equation

Variable z cannot be equal to -2i since division by zero is not defined. Multiply both sides of the equation by z+2i.

$$12\left(z+2i\right)=z-2+1$$

Use the distributive property to multiply 12 by z+2i.

$$12z+24i=z-2+1$$

Add -2 and 1 to get -1.

$$12z+24i=z-1$$

Subtract z from both sides.

$$12z+24i-z=-1$$

Combine 12z and -z to get 11z.

$$11z+24i=-1$$

Subtract 24i from both sides.

$$11z=-1-24i$$

Divide both sides by 11.

$$z=\frac{-1-24i}{11}$$

Divide -1-24i by 11 to get -\frac{1}{11}-\frac{24}{11}i.

$$z=-\frac{1}{11}-\frac{24}{11}i$$