Chapter Contents

• Complex Numbers
• 1. Basic Definitions
• 2. Basic Operations
• 3. Graphical Representation
• 4. Polar Form
• Convert polar to rectangular using calculator
• 5. Exponential Form
• 6. Products and Quotients
• 7. Powers and Roots
• 8. AC Circuit Definitions
• 9. Impedance and Phase Angle
• 10. Reactance and Angular Velocity
• 11. AC Circuit Exercises
• 12. Parallel AC Circuits
• Vocabulary
• Fractals
• Complex Numbers Problem Solver

• Comments, Questions?

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From the math blog...

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^jθ

(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: 2.50e^3.84j

Answer