Algebraic Form of a Complex Locus

Algebraic Form of a Complex Locus

## Formula

If:

$$z=x+iy$$

then:

$$\bar z=x-iy$$

and:

$$z+\bar z=2x$$

$$z-\bar z=2iy$$

Therefore:

$$x=\frac{z+\bar z}{2}$$

$$y=\frac{z-\bar z}{2i}$$

Also:

$$|z|^2=z\bar z$$

## Usage

- Used to convert complex equations into equations in $$x$$ and $$y$$ for identifying loci.