Solve (1+i)x=1+yi

$$( 1 + i ) x = 1 + y i$$

Solve for x

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

Steps for Solving Linear Equation

The equation is in standard form.

$$\left(1+i\right)x=iy+1$$

Divide both sides by 1+i.

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

Dividing by 1+i undoes the multiplication by 1+i.

$$x=\frac{iy+1}{1+i}$$

Divide 1+iy by 1+i.

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

Solve for y

$$y=\left(1-i\right)x+i$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$1+yi=\left(1+i\right)x$$

Subtract 1 from both sides.

$$yi=\left(1+i\right)x-1$$

The equation is in standard form.

$$iy=\left(1+i\right)x-1$$

Divide both sides by i.

$$\frac{iy}{i}=\frac{\left(1+i\right)x-1}{i}$$

Dividing by i undoes the multiplication by i.

$$y=\frac{\left(1+i\right)x-1}{i}$$

Divide \left(1+i\right)x-1 by i.

$$y=\left(1-i\right)x+i$$