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The set of complex numbers, represented by the symbol C, is formed by all numbers that can be written in the form z=a+bi, where a and b are real numbers and i is the imaginary unit. Here, a is called the real part and b is called the imaginary part of the complex number.
If b≠ 0, the number is an imaginary number. Conversely, if b=0, the number is real. Additionally, if a=0 and b≠ 0, the number is a pure imaginary number. Both real and imaginary numbers are subsets of the complex number set.
Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.
a+bi = c+di ⇔ a=c and b=d