Plot point (-3, -3i). Real part -3 on x axis. Imaginary part -3 on y axis. Modulus 3√2 = distance from origin. Argument 225° from positive real axis going anti-clockwise.

To simplify, multiply the numerator and denominator by the conjugate of the denominator, which is $3-i$.

Substitute $i^2 = -1$:

The simplified form of the given complex number is $\boxed{-3i}$.

The student's subsequent calculations for modulus, argument, and plot are based on the complex number $z = -3-3i$. We will proceed with this value.
For $z = -3-3i$, the real part is $a = -3$ and the imaginary part is $b = -3$.
The modulus $|z|$ is given by the formula $|z| = \sqrt{a^2+b^2}$.

The modulus is $\boxed{3\sqrt{2}}$.

To find the argument $\theta$, first find the reference angle $\alpha$ using $\tan(\alpha) = \left|\frac{b}{a}\right|$.

Since the real part $a = -3$ is negative and the imaginary part $b = -3$ is negative, the complex number $z = -3-3i$ lies in the third quadrant.
For a complex number in the third quadrant, the argument $\theta$ is $180^\circ + \alpha$.

The argument is $\boxed{225^\circ}$.

An Argand diagram represents a complex number $z = a+bi$ as a point $(a,b)$ in the complex plane. The horizontal axis represents the real part, and the vertical axis represents the imaginary part.
For $z = -3-3i$, the real part is $-3$ and the imaginary part is $-3$.
Therefore, the complex number is plotted as the point $\boxed{(-3, -3)}$ on the Argand diagram.