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 $x + iy$.