http://www.ck12.org Chapter 11. Complex Numbers
11.3 Trigonometric Polar Form of Complex Numbers
Here you will use basic right triangle trigonometry to represent complex points in the polar plane. You will also use
the trigonometric form of complex numbers to multiply and divide complex numbers.
You already know how to represent complex numbers in the complex plane using rectangular coordinates and you
already know how to multiply and divide complex numbers. Representing these points and performing these
operations using trigonometric polar form will make your computations more efficient.
What are the two ways to multiply the following complex numbers?(
1 +√
3 i)(√
2 −
√
2 i)
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/62127http://www.youtube.com/watch?v=Zha7ZF8aVhU James Sousa: Trigonometric Form of Complex Numbers
Guidance
Any point represented in the complex plane asa+bican be represented in polar form just like any point in the
rectangular coordinate system. You will use the distance from the point to the origin asrand the angle that the point
makes asθ.
As you can see, the pointa+bican also be represented asr·cosθ+i·r·sinθ. The trigonometric polar form can be
abbreviated by factoring out therand noting the first letters: