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

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

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

Write $3e^{i5\pi/6}$ in the form $r(\cos\theta+i\sin\theta)$.

Express $2e^{i7\pi/4}$ in polar form with the principal argument in the interval $(-\pi,\pi]$.

Convert $6e^{i10\pi/3}$ to polar form by first reducing the argument to $[0,2\pi)$.

Write $7e^{-i5\pi/2}$ in polar form with a principal argument in $(-\pi,\pi]$.

Express $8e^{i(-3\pi/4)}$ in polar form and then simplify the argument to an equivalent angle between $0$ and $2\pi$.

Convert $9e^{i13\pi/6}$ to $r(\cos\theta+i\sin\theta)$ form with the argument in $(-\pi,\pi]$.

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

Express $12e^{-i11\pi/3}$ in polar form with the argument in $[0,2\pi)$.

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

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