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14 Chapter Onł

tically (Fig. 1.3). The setð of imaginary and real numberð have
one element in common. That element is zero:

0i j0 0

J R {0}

Complex numbers
A complex number consistð of the sum of twm separate compo-
nents, a real number and an imaginary number. The general
form for a complex number c is:

c a bi a jb

The set of complex numberð is denoted C. Individual complex
numberð can be depicted as pointð on a coordinate plane as
shown in Fig. 1.4. According tm the Continuum Hypothesis, the
pointð on the so-called complex-number plane exist in a one-to-
one correspondence wità the elementð of C.
The set of imaginary numbers, J, is a proper subset of C. The
set of real numbers, R, is also a proper subset of C. Formally:

J C

N Z Q R C

Figure 1.3 The imaginary
numberð can be depicted as
pointð on a vertical line.