IB Mathematics Analysis and Approaches 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 $z$.