19.1. Complex Numbers in Rectangular Form
As usual with any new topic, we start with some definitions.
19.1.1. Imaginary Numbers
Recall that in the real number system, the equation
- x2 = −1
had no solution because there was no real number such that its square was −1. Now we extend our number system to allow the quantity 
to have a meaning. We define the imaginary unit as the square root of −1 and represent it by the symbol i.
As complex numbers find wide use in electric circuits, the letter j is sometimes used for the imaginary unit, reserving i for current.
An imaginary number is the imaginary unit multiplied by a real number. An example of an imaginary number is 9i. In general, we usually denote the real number by b, so the imaginary number would be written as bi.
19.1.2. Complex Numbers
A complex number is any number, real or imaginary, that can be written in the form
- a + bi
where a and b are real numbers, and 
is the imaginary unit. A complex number written this way is said to be in rectangular form.
Example 1:The following numbers are complex numbers in rectangular form.
|
When b = 0 in a complex number a + bi, we have a real number. When a = 0, ...
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