Solve x-2i^2+6i=yi+3xi^3

$$x - 2 i ^ { 2 } + 6 i = y i + 3 x i ^ { 3 }$$

Solve for x

$$x=\left(\frac{3}{10}+\frac{1}{10}i\right)y-2$$

Steps for Solving Linear Equation

Calculate i to the power of 2 and get -1.

$$x-2\left(-1\right)+6i=yi+3xi^{3}$$

Multiply 2 and -1 to get -2.

$$x-\left(-2\right)+6i=yi+3xi^{3}$$

The opposite of -2 is 2.

$$x+2+6i=yi+3xi^{3}$$

Calculate i to the power of 3 and get -i.

$$x+2+6i=yi+3x\left(-i\right)$$

Multiply 3 and -i to get -3i.

$$x+2+6i=yi-3ix$$

Subtract -3ix from both sides.

$$x+2+6i-\left(-3ix\right)=yi$$

Combine x and 3ix to get \left(1+3i\right)x.

$$\left(1+3i\right)x+2+6i=yi$$

Subtract 2 from both sides.

$$\left(1+3i\right)x+6i=yi-2$$

Subtract 6i from both sides.

$$\left(1+3i\right)x=yi-2-6i$$

The equation is in standard form.

$$\left(1+3i\right)x=iy+\left(-2-6i\right)$$

Divide both sides by 1+3i.

$$\frac{\left(1+3i\right)x}{1+3i}=\frac{iy+\left(-2-6i\right)}{1+3i}$$

Dividing by 1+3i undoes the multiplication by 1+3i.

$$x=\frac{iy+\left(-2-6i\right)}{1+3i}$$

Divide iy+\left(-2-6i\right) by 1+3i.

$$x=\left(\frac{3}{10}+\frac{1}{10}i\right)y-2$$

Solve for y

$$y=\left(3-i\right)x+\left(6-2i\right)$$

Steps for Solving Linear Equation

Calculate i to the power of 2 and get -1.

$$x-2\left(-1\right)+6i=yi+3xi^{3}$$

Multiply 2 and -1 to get -2.

$$x-\left(-2\right)+6i=yi+3xi^{3}$$

The opposite of -2 is 2.

$$x+2+6i=yi+3xi^{3}$$

Calculate i to the power of 3 and get -i.

$$x+2+6i=yi+3x\left(-i\right)$$

Multiply 3 and -i to get -3i.

$$x+2+6i=yi-3ix$$

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

$$yi-3ix=x+2+6i$$

Subtract -3ix from both sides.

$$yi=x+2+6i-\left(-3ix\right)$$

Combine x and 3ix to get \left(1+3i\right)x.

$$yi=\left(1+3i\right)x+2+6i$$

The equation is in standard form.

$$iy=\left(1+3i\right)x+\left(2+6i\right)$$

Divide both sides by i.

$$\frac{iy}{i}=\frac{\left(1+3i\right)x+\left(2+6i\right)}{i}$$

Dividing by i undoes the multiplication by i.

$$y=\frac{\left(1+3i\right)x+\left(2+6i\right)}{i}$$

Divide \left(1+3i\right)x+\left(2+6i\right) by i.

$$y=\left(3-i\right)x+\left(6-2i\right)$$