IB Mathematics Analysis and Approaches 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 $r{e}^{i\theta }$.

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

Convert $z=3-\surd 3i$ 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.