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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:

re^j^θ

(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	= re^j^θ
	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: 2.50e^3.84j

Answer

4. Polar Form

6. Products and Quotients

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