Solve z=j/2(1+j)

$$z = \frac { j } { 2 ( 1 + j ) }$$

Solve for j

$$j=-\frac{2z}{2z-1}$$

$$z\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Variable j cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by 2\left(j+1\right).

$$z\times 2\left(j+1\right)=j$$

Use the distributive property to multiply z\times 2 by j+1.

$$2zj+z\times 2=j$$

Subtract j from both sides.

$$2zj+z\times 2-j=0$$

Subtract z\times 2 from both sides. Anything subtracted from zero gives its negation.

$$2zj-j=-z\times 2$$

Multiply -1 and 2 to get -2.

$$2zj-j=-2z$$

Combine all terms containing j.

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

Divide both sides by 2z-1.

$$\frac{\left(2z-1\right)j}{2z-1}=-\frac{2z}{2z-1}$$

Dividing by 2z-1 undoes the multiplication by 2z-1.

$$j=-\frac{2z}{2z-1}$$

Variable j cannot be equal to -1.

$$j=-\frac{2z}{2z-1}\text{, }j\neq -1$$

Solve for z

$$z=\frac{j}{2\left(j+1\right)}$$

$$j\neq -1$$