Solve (3-4i)^2-2(x-yi)=x+yi

$$( 3 - 4 i ) ^ { 2 } - 2 ( x - y i ) = x + y i$$

Solve for x

$$x=\frac{iy}{3}+\left(-\frac{7}{3}-8i\right)$$

Steps for Solving Linear Equation

Calculate 3-4i to the power of 2 and get -7-24i.

$$-7-24i-2\left(x-yi\right)=x+yi$$

Subtract x from both sides.

$$-7-24i-2\left(x-yi\right)-x=yi$$

Multiply -1 and i to get -i.

$$-7-24i-2\left(x-iy\right)-x=yi$$

Use the distributive property to multiply -2 by x-iy.

$$-7-24i-2x+2iy-x=yi$$

Combine -2x and -x to get -3x.

$$-7-24i-3x+2iy=yi$$

Add 7+24i to both sides.

$$-3x+2iy=yi+\left(7+24i\right)$$

Subtract 2iy from both sides.

$$-3x=yi+\left(7+24i\right)-2iy$$

Combine yi and -2iy to get -iy.

$$-3x=-iy+\left(7+24i\right)$$

The equation is in standard form.

$$-3x=7+24i-iy$$

Divide both sides by -3.

$$\frac{-3x}{-3}=\frac{7+24i-iy}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x=\frac{7+24i-iy}{-3}$$

Divide -iy+\left(7+24i\right) by -3.

$$x=\frac{iy}{3}+\left(-\frac{7}{3}-8i\right)$$

Solve for y

$$y=24-7i-3ix$$

Steps for Solving Linear Equation

Calculate 3-4i to the power of 2 and get -7-24i.

$$-7-24i-2\left(x-yi\right)=x+yi$$

Subtract yi from both sides.

$$-7-24i-2\left(x-yi\right)-yi=x$$

Multiply -1 and i to get -i.

$$-7-24i-2\left(x-iy\right)-yi=x$$

Use the distributive property to multiply -2 by x-iy.

$$-7-24i-2x+2iy-yi=x$$

Multiply -1 and i to get -i.

$$-7-24i-2x+2iy-iy=x$$

Combine 2iy and -iy to get iy.

$$-7-24i-2x+iy=x$$

Add 7+24i to both sides.

$$-2x+iy=x+\left(7+24i\right)$$

Add 2x to both sides.

$$iy=x+\left(7+24i\right)+2x$$

Combine x and 2x to get 3x.

$$iy=3x+\left(7+24i\right)$$

Divide both sides by i.

$$\frac{iy}{i}=\frac{3x+\left(7+24i\right)}{i}$$

Dividing by i undoes the multiplication by i.

$$y=\frac{3x+\left(7+24i\right)}{i}$$

Divide 3x+\left(7+24i\right) by i.

$$y=24-7i-3ix$$