Solve (i-2)i+jx=x/1+i+2

$$( i - 2 ) i + j x = \frac { x } { 1 + i } + 2$$

Solve for j

$$j=\frac{1}{2}-\frac{1}{2}i+\frac{3+2i}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply i-2 by i.

$$-1-2i+jx=\frac{x}{1+i}+2$$

Add 1+2i to both sides.

$$jx=\frac{x}{1+i}+2+\left(1+2i\right)$$

Do the additions in 2+\left(1+2i\right).

$$jx=\frac{x}{1+i}+3+2i$$

The equation is in standard form.

$$xj=\left(\frac{1}{2}-\frac{1}{2}i\right)x+\left(3+2i\right)$$

Divide both sides by x.

$$\frac{xj}{x}=\frac{\left(\frac{1}{2}-\frac{1}{2}i\right)x+\left(3+2i\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$j=\frac{\left(\frac{1}{2}-\frac{1}{2}i\right)x+\left(3+2i\right)}{x}$$

Divide \left(\frac{1}{2}-\frac{1}{2}i\right)x+\left(3+2i\right) by x.

$$j=\frac{1}{2}-\frac{1}{2}i+\frac{3+2i}{x}$$

Solve for x

$$x=\frac{6+4i}{2j+\left(-1+i\right)}$$

$$j\neq \frac{1}{2}-\frac{1}{2}i$$