Question Type 1: Converting from Cartesian to Euler and Polar Exercises

Express $z = -2 - 2i$ in polar and Euler form.

Convert $z = 1 - i$ into polar form and Euler form, specifying $\theta$ explicitly.

Express $z = -1 + \sqrt{3}i$ in both polar and Euler forms, with exact angles.

Express $z = -4 + 3i$ in polar form and Euler form, giving the argument in the correct quadrant.

Convert the complex number $4 + 3i$ to polar form $r(\cos\theta + i\sin\theta)$ and Euler form $re^{i\theta}$.

Find the polar form and Euler form of $z = -5i$. [4]

Convert $z = 3 - √{3}i$ to polar and Euler forms, giving exact values.

Find the polar and Euler forms of $z = -3 - 3i$.

Convert $z = 5i$ to polar and Euler forms.

Determine the modulus-argument (polar) form and exponential form of the complex number $z = -\sqrt{3} + i$, giving the argument $\theta$ in the interval $-\pi < \theta \le \pi$.

Express $z = \sqrt{3} + i$ in polar form and Euler form, with $\theta$ in simplest exact form.

Convert $z = 2\sqrt{2} - 2\sqrt{2}\,i$ to polar and Euler forms.