Express the complex number $\space -\sqrt{3}+i\space$, in the polar form.

Find the area of the triangle described. $a=9, b=40, c=41$

Solve the below given triangle :

$$\alpha=80^{\circ}, \gamma=30^{\circ}, b=3 \mathrm{ft}$$

Find the angle (round to the nearest degree) between the pair of vectors: $\newline$ $\langle{ - 2, - 3\rangle}$ and $\langle{ - 3, 4\rangle}$

find the magnitude and direction angle of the given vector. $\textbf{u}=\langle{\sqrt{3},3}\rangle$

Find the quotient $\frac{z_1}{z_2}$ and express it in rectangular form.

$$z_1 = \sqrt{12}(\cos 350\degree + i \sin 350\degree) \text{ and } z_2 = \sqrt{3} (\cos 80\degree + i \sin 80\degree)$$

Convert the point $(-4,4)$, to exact polar coordinates. Assume that $0\le \theta < {2\pi}$.

Two sides and an angle are given below. Determine whether a triangle (or two) exist and, if so, solve the triangle.

$$a=40, b=30, \beta=150^{\circ}$$

Express the complex number $\space \sqrt{3}-3i\space$, in the polar form.

Solve the below triangle:

$$a=9, c=12, \beta=23^{\circ}$$

Solve the below given triangle :

$$\beta=26^{\circ}, \gamma=57^{\circ}, c=100 \mathrm{yd}$$

Find the quotient $\frac{z_1}{z_2}$ and express it in rectangular form.

$$z_1 = 4(\cos 280\degree + i \sin 280\degree) \text{ and } z_2 = 4(\cos 55\degree + i \sin 55\degree)$$

Find the angle (round to the nearest degree) between the pair of vectors: $\newline$ $\langle{2, - 4\rangle}$ and $\langle{4, - 1\rangle}$

Convert the point $(6,6\sqrt3)$, to exact polar coordinates. Assume that $0\le \theta < {2\pi}$.