Tool for calculating the value of the modulus of a complex number. The modulus of a complex number \( z \) is written \( | z | \) (absolute value) and consists of the length of the segment between the point of origin of the complex plane and the point \( z \).

Complex Number Modulus - dCode

Tag(s) : Mathematics

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

This page is using the new English version of dCode, *please make comments* !

Sponsored ads

Tool for calculating the value of the modulus of a complex number. The modulus of a complex number \( z \) is written \( | z | \) (absolute value) and consists of the length of the segment between the point of origin of the complex plane and the point \( z \).

The module is the length (absolute value) qualifying the complex number \( z = a + ib \) (with \( a \) the real part and \( b \) the imaginary part), it is denoted \( | z | \) and is equal to \( | z | = \sqrt{a ^ 2 + b ^ 2} \).

Example: Consider \( z = 1+i \) (of abscissa 1 and of ordinate 1 on the complex plane) then the modulus equals \( |z| = \sqrt{1^2+1^2} = \sqrt{2} \)

The module of a real number is equivalent to its absolute value.

Consider the complex numbers \(z, z_1, z_2 \), the complex module has the following properties:

$$ |z_1 \cdot z_2| = |z_1| \cdot |z_2| $$

$$ \left| \frac{z_1}{z_2} \right| = \frac{|z_1|}{|z_2|} \iff z_2 \ne 0 $$

$$ |z_1+z_2| \le |z_1|+|z_2| $$

A modulus is an absolute value, therefore necessarily positive (or null):

$$ |z| \ge 0 $$

The modulus of a complex number and its conjugate are equal:

$$ |\overline z|=|z| $$

dCode retains ownership of the source code of the script Complex Number Modulus. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Complex Number Modulus script for offline use, for you, your company or association, see you on contact page !

modulus,complex,number,value,plane,calculator

Source : http://www.dcode.fr/complex-number-modulus

© 2017 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode