Polar Form of Complex Numbers

Practice Questions

Trigonometry › Polar Form of Complex Numbers

Questions

The polar coordinates $\left ( r,\theta \right )$ of a point are $\left(2.1, \frac{7\pi }{3}\right )$ . Convert these polar coordinates to rectangular coordinates.

Find the following quotients, given that $z_1=10(\cos40^\circ+i\sin40^\circ)$ and $z_2=2(\cos220^\circ-i\sin220^\circ)$ . Give results in both polar and rectangular forms.

(a) $\frac{z_1}{z_2}$

(b) $\frac{z_2}{z_1}$

Express the complex number $z=4(\cos240^\circ+i\sin240^\circ)$ in rectangular form.

Multiply the following complex numbers (in polar form), giving the result in both polar and rectangular form.

$2(\cos70^\circ+i\sin70^\circ)\cdot 3(\cos20^\circ+i\sin20^\circ)$

For the complex number , find the modulus $r=\sqrt{x^2+y^2}$ and the angle $\theta=\tan^-^1\left (\frac{y}{x} \right )$ . Then, express this number in polar form $z=r(\cos\theta+i\sin\theta)$ .

Express the complex number $z=3(\cos30^\circ+i\sin30^\circ)$ in rectangular form .

Express the complex number in polar form.

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