Complex Numbers • Section 6.3 139 6.3 Complex Numbers There is no real number x such that x 2 = − 1. However, it turns out to be useful 6 to invent such a number, called the imaginary unit and denoted by the letter i . Thus, i 2 = − 1, and hence i = r − 1. If a and b are real numbers, then a number of the form a + bi is called a complex number , and if b n= 0 then it is called an imaginary number (and pure imag-inary if a = 0 and b n= 0). The real number a is called the imaginary part of the complex number a + bi , and bi is called its imaginary part . What does it mean to add a to bi in the deFnition a + bi of a complex number, i.e. adding a real number and an imaginary number? You can think of it as a way of extending the set of real numbers. If b = 0 then a + bi = a +0 i = a (since 0 i is deFned as 0), so that every real number is a complex number. The imaginary part bi in a + bi can be thought of as a way of taking the one-dimensional set of all real numbers and extending it to a
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.