By Kardi Teknomo, PhD .
ComplexNumber

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What is Complex Number?

To understand where Complex Number is located in Number Theory, here is a tree diagram.

Complex Number Tutorial: What is Complex Number?

Complex Number is the most general set of numbers that cover all numbers. All numbers are Complex Numbers.

Complex Number consist of 2 parts:

1. Real part

2. Imaginary part

When the imaginary part is zero, we have only the real part, thus we have Real Numbers. In other words, Real Number is a subset of Complex Number.

Real Number consists of Rational Number and Irrational Number. Rational Number consist of Integers and Fractions. Integer consists of Positive Integers and Negative Integer and Zero. (Similarly Fraction can also be seen as positive and negative but I do not show in the diagram above). The set of Positive Integers is also called Natural Numbers. Set of Positive integers and zero is called Whole Numbers.

You see that the imaginary part of Complex Numbers is the distinguished term between Complex Numbers and purely Real Numbers. Let us define a special imaginary operator denoted as Complex Number Tutorial: What is Complex Number? to be

Complex Number Tutorial .

Thus, we can also define it as

Complex Number Tutorial: What is Complex Number?

A complex number Complex Number Tutorial: What is Complex Number? is defined as Complex Number Tutorial .

The real part is Complex Number Tutorial .

The imaginary part is Complex Number Tutorial . Note that the imaginary part by itself, without the imaginary operator Complex Number Tutorial , is a real number.

When the imaginary part is zero, we only have the real part and we write it as Complex Number Tutorial: What is Complex Number? instead of Complex Number Tutorial . When the real part is zero, we write it as Complex Number Tutorial instead of Complex Number Tutorial .

See Also : Euler Formula , Complex Plane , Magnitude and Direction

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