# Polar form of complex numbers

### Polar form of complex numbers

Knowing the argument and the modulus of a complex number allows us to convert a complex number from its rectangular form, which is what we have been using thus far, to its other basic form – polar form. We will see that while a complex number in rectangular form is denoted by its horizontal and vertical components, a complex number in polar form is denoted by its magnitude and argument.

#### Lessons

• 1.
Convert the following complex numbers from rectangular form to polar form
a)
$z=2i-3$

b)
$w=-5-3i$

c)
$z=4-i$

• 2.
Convert the following complex numbers from polar form to rectangular form
a)
$z=4(\cos(\frac{\pi}{4})+i\sin(\frac{\pi}{4}))$

b)
$w=13(\cos(180^{\circ})+i\sin(180^{\circ}))$

c)
$z=4(\cos(\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))$

• 3.
Given that $z=4-3i$, and $w=2-i$, find $z+w$ and express it in polar form