IB Mathematics Analysis and Approaches Question Type 2: Converting from Euler to Polar and from Polar to Cartesian Exercises

Convert $z=6\text{cis}\left(-\frac{\pi }{6}\right)$ to Cartesian form $x+iy$.

Express $z=9e^{i5\pi /4}$ in polar form $r\text{cis}(\theta )$.

Convert $z=7\text{cis}\left(-\frac{2\pi }{3}\right)$ to Cartesian form $x+iy$.

Express $z=2\sqrt{2}{e}^{i\frac{3\pi }{4}}$ in polar form $r\text{cis}(\theta )$.

Convert $z=8\text{cis}\frac{5\pi }{4}$ to Cartesian form $x+iy$.

Convert $z=10\text{cis}\frac{3\pi }{2}$ to Cartesian form $x+iy$.

Express $z=10e^{i\frac{3\pi }{2}}$ in polar form $r\text{cis}\theta$.

Convert $z=3\text{cis}\frac{\pi }{3}$ to Cartesian form $x+iy$.

Express $z=e^{i\pi }$ in polar form $r\text{ cis }\theta$.

Express $z=3e^{\frac{i\pi }{3}}$ in polar form $r\text{cis}(\theta )$.

Express $z=4e^{i\frac{\pi }{4}}$ in polar form $r\text{cis}(\theta )$.

Convert $z=2\sqrt{2}\text{cis}\left(\frac{3\pi }{4}\right)$ to Cartesian form $x+iy$.

Express $z=5e^{-i\frac{\pi }{6}}$ in polar form $r\text{cis}(\theta )$.

Express $z=7e^{-i\frac{2\pi }{3}}$ in polar form $r\text{cis}(\theta )$.

Convert $z=4\text{cis}\left(\frac{\pi }{4}\right)$ to Cartesian form $x+iy$.

Convert $z=5\text{cis}(\pi )$ to Cartesian form $x+iy$.