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.
Example 2.
Express -1 + 5j in exponential form.
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°)
2. Express in exponential form: -1 - 5j
3. Express in polar and rectangular forms: 2.50e3.84j
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