Solve x+yi=(-4)^frac{1{2}}

$$x + y i = ( - 4 ) ^ { \frac { 1 } { 2 } }$$

Solve for x

$$x=2i-iy$$

Solution Steps

Calculate -4 to the power of \frac{1}{2} and get 2i.

$$x+yi=2i$$

Subtract yi from both sides.

$$x=2i-yi$$

Multiply -1 and i to get -i.

$$x=2i-iy$$

Solve for y

$$y=ix+2$$

Steps for Solving Linear Equation

Calculate -4 to the power of \frac{1}{2} and get 2i.

$$x+yi=2i$$

Subtract x from both sides.

$$yi=2i-x$$

The equation is in standard form.

$$iy=2i-x$$

Divide both sides by i.

$$\frac{iy}{i}=\frac{2i-x}{i}$$

Dividing by i undoes the multiplication by i.

$$y=\frac{2i-x}{i}$$

Divide 2i-x by i.

$$y=ix+2$$