Solve left(3+4iright)^2-2left(x-yright)=x+y

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

Solve for x

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

Steps for Solving Linear Equation

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

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

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

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

Subtract x from both sides.

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

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

$$-7+24i-3x+2y=y$$

Subtract -7+24i from both sides.

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

Subtract 2y from both sides.

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

Multiply -1 and -7+24i to get 7-24i.

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

Combine y and -2y to get -y.

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

The equation is in standard form.

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

Divide both sides by -3.

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

Dividing by -3 undoes the multiplication by -3.

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

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

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

Solve for y

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

Solution Steps

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

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

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

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

Subtract y from both sides.

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

Combine 2y and -y to get y.

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

Subtract -7+24i from both sides.

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

Add 2x to both sides.

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

Multiply -1 and -7+24i to get 7-24i.

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

Combine x and 2x to get 3x.

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