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) : Arithmetics, Geometry

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*!

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

The calculation also applies with the exponential form of the complex number.

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

Example: \( |-3| = 3 \)

For 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 online. 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, Matlab, etc.) which dCode owns rights will not be given for free. To download the online Complex Number Modulus script for offline use on PC, iPhone or Android, ask for price quote on contact page !

modulus,complex,number,value,plane,calculator

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

© 2018 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback