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 $re^{i\theta}$.

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.