Question Type 4: Calculating argument of complex numbers Exercises

Compute the argument of $z = -2i$.

Determine the argument of the complex number given in polar form: $z=7 \text{cis}\left(-\frac{\pi}{3}\right)$

Find the principal argument of $z=\frac{2 - i}{1 + 2i}.$

Find the principal argument of $z = 1 - \sqrt{3}\,i$.

Find the principal argument of $z = 3 + 3i$.

Find the principal argument of the complex number $z = 2 - 3i$.

Find the principal argument of $z = -\sqrt{3} - i$.

Calculate the argument of $z = -1 + \sqrt{3}\,i$ in the interval $(0,2\pi)$.

Let $z=-1+2i$. Find $\arg(z)$ and then compute $\arg(z^3)$ (principal values).

Calculate the argument of the product $z = (1 + i)(1 - i)$.

Compute the argument of $z = i$.

Show that for $z=1+\sqrt{3}i$, the argument of $z^2$ is twice the argument of $z$.