Question Type 2: Converting complex numbers from Euler to Polar form Exercises

Express $z$ in the form $r(\cos \theta + i \sin \theta)$, where $r > 0$ and $0 \leq \theta < 2\pi$.

Write $7\mathrm{e}^{-\mathrm{i}5\pi/2}$ in polar form with a principal argument in $(-\pi, \pi]$.

Convert $9\text{e}^{\text{i}\frac{13\pi}{6}}$ to $r(\cos\theta + \text{i}\sin\theta)$ form with the argument in $(-\pi, \pi]$.

Convert $6e^{i\frac{10\pi}{3}}$ to polar form by first reducing the argument to $[0, 2\pi)$.

Write $14e^{i17\pi/5}$ in trigonometric form, reducing the argument to the interval $[0,2\pi)$.

Convert $5e^{-i\frac{\pi}{3}}$ to polar form $r(\cos\theta+i\sin\theta)$.

Express $8e^{i\left(-\frac{3\pi}{4}\right)}$ in the polar form $r(\cos \theta + i \sin \theta)$, where $0 \le \theta < 2\pi$.

Write $10e^{i15\pi/4}$ in polar form by reducing its argument to the range $(-\pi,\pi]$.

Express $2e^{i\frac{7\pi}{4}}$ in polar form with the principal argument in the interval $(-\pi,\pi]$.

Express $4e^{i\frac{\pi}{4}}$ in polar form $r(\cos\theta+i\sin\theta)$.

Convert $5e^{i\left(-\frac{13\pi}{4}\right)}$ to $r(\cos\theta + i\sin\theta)$ form, giving the principal argument in the interval $(-\pi, \pi]$.

Write $3\text{e}^{\text{i}\frac{5\pi}{6}}$ in the form $r(\cos\theta + \text{i}\sin\theta)$.