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...

Converting Complex Numbers

Polar to Rectangular Forms Using Calculator

Example 1

Convert 56 ∠ 27° to rectangular form (x + jy).

Keystrokes	Display
56	56
	56
27	27
	49.89636535 (= x)
	25.42346799 (= y)

Therefore, 56 ∠ 27° ≈ 49.9 + 25.4 j

We have converted a complex number from polar form (using degrees) into rectangular form.

Of course, you have to be careful that you have your calculator set correctly in degrees (or radians, if required).

Example 2

Convert 12 - 42j to polar form (r ∠ q).

For CASIO calculator...

Keystrokes	Display
12	12
	12
42	42
	-42
	43.68065934 (= r)
	-74.0546041 (= θ)

Therefore,

Complex number in rectangular form:	12 - 42j
Same complex number in polar form:	43.7 ∠ -74°

---

For Sharp calculator, it is a similar process.

Consult your calculator manual for full details.