Solve z/z-8=-1-2i

$$\frac { z } { z - 8 } = - 1 - 2 i$$

Solve for z

$$z=6+2i$$

Steps for Solving Linear Equation

Variable z cannot be equal to 8 since division by zero is not defined. Multiply both sides of the equation by z-8.

$$z=\left(-1-2i\right)\left(z-8\right)$$

Use the distributive property to multiply -1-2i by z-8.

$$z=\left(-1-2i\right)z+\left(8+16i\right)$$

Subtract \left(-1-2i\right)z from both sides.

$$z-\left(-1-2i\right)z=8+16i$$

Combine z and \left(1+2i\right)z to get \left(2+2i\right)z.

$$\left(2+2i\right)z=8+16i$$

Divide both sides by 2+2i.

$$z=\frac{8+16i}{2+2i}$$

Multiply both numerator and denominator of \frac{8+16i}{2+2i} by the complex conjugate of the denominator, 2-2i.

$$z=\frac{\left(8+16i\right)\left(2-2i\right)}{\left(2+2i\right)\left(2-2i\right)}$$

Do the multiplications in \frac{\left(8+16i\right)\left(2-2i\right)}{\left(2+2i\right)\left(2-2i\right)}.

$$z=\frac{48+16i}{8}$$

Divide 48+16i by 8 to get 6+2i.

$$z=6+2i$$