NPTEL IIT Guwahati

Modulus of a Complex Number: The absolute value or modulus of a complex number is denoted by $\vert z \vert$ and is given by

MATH

Here, as usual, the radical stands for the principal (non-negative) square root of $x^{2} + y^{2}$ .

Note that $\vert z \vert$ is always a non-negative real number and that the only complex number whose modulus is zero is the number . Basically the above definition extends the concept of absolute value of a real number to the complex number system.
Example: The modulus of the complex number is .

Properties:
1. and $\vert z \vert = 0$ iff .
2. .
3. .


Complex Numbers and Complex Algebra: Modulus of a Complex Number		Print this page
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Modulus of a Complex Number: The absolute value or modulus of a complex number is denoted by $\vert z \vert$ and is given by Here, as usual, the radical stands for the principal (non-negative) square root of $x^{2} + y^{2}$ . Note that $\vert z \vert$ is always a non-negative real number and that the only complex number whose modulus is zero is the number . Basically the above definition extends the concept of absolute value of a real number to the complex number system. Example: The modulus of the complex number is . Properties: 1. and $\vert z \vert = 0$ iff . 2. . 3. .

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