5. Exponential Form of a Complex Number

by M. Bourne


IMPORTANT:

In this section, θ MUST be expressed in radians.

We use the important constant

e = 2.718 281 8...

in this section.

We first met e in the section Natural logarithms (to the base e).

The exponential form of a complex number is:

rejθ

(r is the absolute value of the complex number, the same as we had before and θ is in radians.)

 

Example 1:

Express 5(cos 135°+ j sin 135°) in exponential form.


Answer


Example 2.

Express -1 + 5j in exponential form.


Answer


SUMMARY: Forms of a complex number

Rectangular form Polar form Exponential form
x + yj = r(cos θ+ jsin θ) = r cis θ = r∠θ = rejθ
θ can be in degrees OR radians θ MUST be in radians

 

Exercises

1. Express in exponential form:

4.50(cos282.3°+ j sin 282.3°)


Answer


2. Express in exponential form: -1 - 5j


Answer


3. Express in polar and rectangular forms: 2.50e3.84j


Answer




get MathTutorDVDs

Easy to understand math lessons on DVD. Try before you commit.
MathTutorDVD.com


Book mark this page in Del.icio.us, Furl, Digg, StumbleUpon, whatever...


Didn't find what you are looking for? Try search:


Need a break? Play a math game. Well, they all involve math... No, really!

dumbolf memoTST bola shadow factory mindfields trick-hoops-challenge crystal clear