For a complex number z = x + jy:

$$\tan \theta = \frac{4}{2} = 2$$ $$\theta = \arctan(2) \approx 1.107 \text{ radians} \quad (\text{or } 63.43^\circ)$$

Since $x>0$ and $y>0$, $\theta$ is in the first quadrant, so this is the principal argument.

$$\boxed{\text{Modulus} = 2\sqrt{5}, \text{ Argument} \approx 1.107 \text{ rad}}$$

First, find the reference angle $\alpha = \arctan\left(\left|\frac{y}{x}\right|\right)$.

$$\alpha = \arctan\left(\left|\frac{-2}{-5}\right|\right) = \arctan\left(\frac{2}{5}\right) \approx 0.3805 \text{ radians} \quad (\text{or } 21.80^\circ)$$

Since $x<0$ and $y<0$, the argument $\theta$ is in the third quadrant. For the principal argument, we subtract $\pi$ from the reference angle (or $180^\circ$).

$$\theta = \alpha - \pi \approx 0.3805 - \pi \approx -2.761 \text{ radians} \quad (\text{or } 21.80^\circ - 180^\circ = -158.20^\circ)$$ $$\boxed{\text{Modulus} = \sqrt{29}, \text{ Argument} \approx -2.761 \text{ rad}}$$

$$\tan \theta = \frac{2}{1} = 2$$ $$\theta = \arctan(2) \approx 1.107 \text{ radians} \quad (\text{or } 63.43^\circ)$$

Since $x>0$ and $y>0$, $\theta$ is in the first quadrant, so this is the principal argument.

$$\boxed{\text{Modulus} = \sqrt{5}, \text{ Argument} \approx 1.107 \text{ rad}}$$