#### Answer

The graph of all the complex numbers, $z$, will be a straight line passing through the origin with $y = x$ and slope = 1 (argument $\theta = 45^\circ$).

#### Work Step by Step

For $z = x+yi$,
The real and imaginary parts of z are equal, shall mean,
$y = x$
The graph of all the complex numbers, $z$, satisfying the captioned condition will be a straight line passing through the origin with $y = x$ and slope = 1 (argument $\theta = 45^\circ$).