Introductory Electrical Engineering With Math Explained in Accessible Language

Appendix DComplex Numbers

D.1 Real Numbers

Real numbers can be seen as numbers that exist in a horizontal line. Zero is at the center. Positive numbers extend to the right and negative numbers to the left, like shown in Figure D.1.

Figure D.1 Real numbers.

D.2 Complex Numbers

A complex number is represented by two axes, a real (horizontal) and an imaginary (vertical) one, like shown in Figure D.2.

This characteristic of complex numbers provides these numbers with the ability to express three quantities: two numerical values and an angle.

An imaginary number has the following form, called a rectangular form.

• where a is the real part and b the imaginary part.
• The imaginary part is represented with a letter, generally i or j.

Figure D.2 Imaginary number axes.

Figure D.3 Imaginary number example.

3 + 2i is an imaginary number that can be represented on the complex number plane as seen in Figure D.3.

D.2.1 Operations with Complex Numbers

D.2.1.1 Addition

To add two complex numbers, the real and the imaginary parts must be added alone.

Therefore,

D.2.1.2 Subtraction ...