IB Mathematics Applications & Interpretation Question Type 1: Converting Complex Numbers from Cartesian Form to Euler and Polar Forms Exercises

Express $z$ in:

(a) polar form $r(\cos \theta +i\sin \theta )$, where $\theta$ is in radians.

(b) Euler form $r{e}^{i\theta }$.

Convert $z=-1-\sqrt{3}i$ to polar form $r\angle \theta$ (degrees) and Euler form.

Convert $z=1+\sqrt{3}i$ into polar form $r\angle \theta$ (in degrees) and Euler form.

Express $z=-1+\sqrt{3}i$ in polar form $r(\cos \theta +i\sin \theta )$ and Euler form, with $\theta$ in radians.

Express $z=-3$ in polar and Euler forms.

Express $z=-5i$ in the form $r(\cos \theta +i\sin \theta )$ and in Euler form.

Find the polar and Euler forms of $z=\sqrt{3}-i$, with angle in radians.

Convert $z=2-2\sqrt{3}i$ into polar form $r(\cos \theta +i\sin \theta )$ and Euler form (radians).

Express $z=-4-4i$ in polar form and Euler form, giving the argument in radians.

Convert $z=3$ into polar and Euler forms.

Express $z=-2+2\sqrt{3}i$ in polar and Euler forms, with argument in radians.

Convert the purely imaginary number $z=5i$ into polar and Euler forms.