#### Answer

The graph of all the complex numbers, $z$, will be a unit circle of radius 1 centered at the origin (0,0). It include all the complex numbers of absolute value 1, and each has the equation $|z|$ = 1.

#### Work Step by Step

For $z = x + yi$,
The absolute value of $z$ is 1, shall mean,
$|z|$ = 1, or
$|z|$ = $\sqrt{x^2 + y^2} = 1$
The graph of all the complex numbers, $z$, satisfying the captioned condition will be a unit circle of radius 1 centered at the origin (0,0). It include all the complex numbers of absolute value 1, and each has the equation $|z|$ = 1.