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

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

Solve for z

$$z=-\frac{2}{11}-\frac{23}{11}i\approx -0.181818182-2.090909091i$$

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.

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

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

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

Subtract z from both sides.

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

Combine 12z and -z to get 11z.

$$11z+24i=-2+i$$

Subtract 24i from both sides.

$$11z=-2+i-24i$$

Subtract 24i from -2+i to get -2-23i.

$$11z=-2-23i$$

Divide both sides by 11.

$$z=\frac{-2-23i}{11}$$

Divide -2-23i by 11 to get -\frac{2}{11}-\frac{23}{11}i.

$$z=-\frac{2}{11}-\frac{23}{11}i$$