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, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

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 modulus 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} $.

The module can be interpreted as the distance separating the point (representing the complex number) from the origin of the reference of the complex plane.

To find the module of a complex number $ z = a + ib $ carry out the computation $ |z| = \sqrt {a^2 + b^2} $

Example: $ z = 1+2i $ (of abscissa 1 and of ordinate 2 on the complex plane) then the modulus equals $ |z| = \sqrt{1^2+2^2} = \sqrt{5} $

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

The modulus (or magnitude) of a real number is equivalent to its absolute value.

Example: $ |-3| = 3 $

For the complex numbers $ z, z_1, z_2 $ the **complex modulus** has the following properties:

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

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

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

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 released 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,magnitude,complex,number,value,plane,calculator

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

© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback

▲