# Operations on complex numbers in polar form

##### Examples

###### Lessons

- Multiplying complex numbers in polar form
- $4(\cos(\frac{5\pi}{3})+i \sin(\frac{5\pi}{3})) \cdot 8(\cos(\frac{2\pi}{3})+i \sin(\frac{2\pi}{3}))$
- $(\cos(170^{\circ})+i \sin(170^{\circ}))\cdot 5(\cos(45^{\circ})+i \sin(45^{\circ}))$
- $3(\cos(\pi)+i \sin(\pi))\cdot(\cos(\frac{\pi}{5})+i \sin(\frac{\pi}{5}))\cdot6(\cos(\frac{2\pi}{3})+i \sin(\frac{2\pi}{3}))$

- Dividing complex numbers in polar form
- Convert the following complex number to exponential form

$z=3+i$

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###### Topic Notes

Let's find out how to perform some basic operations on complex numbers in polar form! We will briefly introduce the notion of the exponential form of a complex number, then we will focus on multiplication and division on complex numbers in polar form.

Note:

Polar form real part$a=|z|\cos \theta$

imaginary part$b=|z|\sin \theta$

$z=|z|(\cos \theta+i\sin \theta)$

When …

Multiplying:

Dividing:

Exponential form$z=|z|e^{i \theta}$

Polar form real part$a=|z|\cos \theta$

imaginary part$b=|z|\sin \theta$

$z=|z|(\cos \theta+i\sin \theta)$

When …

Multiplying:

*multiply*the absolute values, and*add*the anglesDividing:

*divide*the absolute values, and*subtract*the anglesExponential form$z=|z|e^{i \theta}$

###### Basic Concepts

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