Solve z_{7}=1/2+j

$$z _ { 7 } = \frac { 1 } { 2 + j }$$

Solve for j

$$j=-2+\frac{1}{z_{7}}$$

$$z_{7}\neq 0$$

Steps for Solving Linear Equation

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

$$z_{7}\left(j+2\right)=1$$

Use the distributive property to multiply z_{7} by j+2.

$$z_{7}j+2z_{7}=1$$

Subtract 2z_{7} from both sides.

$$z_{7}j=1-2z_{7}$$

Divide both sides by z_{7}.

$$\frac{z_{7}j}{z_{7}}=\frac{1-2z_{7}}{z_{7}}$$

Dividing by z_{7} undoes the multiplication by z_{7}.

$$j=\frac{1-2z_{7}}{z_{7}}$$

Divide 1-2z_{7} by z_{7}.

$$j=-2+\frac{1}{z_{7}}$$

Variable j cannot be equal to -2.

$$j=-2+\frac{1}{z_{7}}\text{, }j\neq -2$$

Solve for z_7

$$z_{7}=\frac{1}{j+2}$$

$$j\neq -2$$