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




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