Search for a tool
Complex Number Conjugate

Tool for calculating the value of the conjugate of a complex number. The conjugate of a complex number \( z \) is written \( \overline{z} \) or \( z^* \) and is formed of the same real part with an opposite imaginary part.

Results

Complex Number Conjugate -

Tag(s) : Mathematics

dCode and you

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!


Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Complex Number Conjugate tool. Thank you.

  >  [News]: Discover the next version of dCode Complex Number Conjugate!

Complex Number Conjugate

Sponsored ads

Complex Conjugate Calculator


Tool for calculating the value of the conjugate of a complex number. The conjugate of a complex number \( z \) is written \( \overline{z} \) or \( z^* \) and is formed of the same real part with an opposite imaginary part.

Answers to Questions

How to calculate the conjugate of a complex number?

The conjugate of a complex number \( z = a+ib \) is noted with a bar \( \overline{z} \) (or sometimes with a star \( z^* \)) and is equal to \( \overline{z} = a-ib \) with \( a = \Re{z} \) the real part and \( b = \Im{z} \) the imaginary part.

Example: Consider \( z = 1 + i \) then the conjugate is \( \overline{z} = 1-i \)

On a complex plane, the points \( z \) and \( \overline{z} \) are symmetrical (symmetry with respect to the abscissa x-axis), the 2 points are conjugate pairs.

What are the properties of conjugates?

Using the complex numbers \( z, z_1, z_2 \), the conjugate has the following properties:

$$ \overline{z_1+z_2} = \overline{z_1} + \overline{z_2} $$

$$ \overline{z_1 \cdot z_2} = \overline{z_1} \times \overline{z_2} $$

$$ \overline{\left(\frac{z_1}{z_2}\right)} = \frac{\overline{z_1}}{\overline{z_2}} \iff z_2 \neq 0 $$

A number without an imaginary part is equal to its conjugate:

$$ \Im(z) = 0 \iff \overline{z} = z $$

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

$$ |\overline{z}|=|z| $$

How to calculate the conjugate of a real number?

The conjugate \( \overline{a} \) of a real number \( a \) is the number \(a\) itself: \( a=a+0i=a-0i=\overline{a} \)

Source code

dCode retains ownership of the source code of the script Complex Number Conjugate 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 Conjugate script for offline use on PC, iPhone or Android, ask for price quote on contact page !

Questions / Comments

  >  [News]: Discover the next version of dCode Complex Number Conjugate!


Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Complex Number Conjugate tool. Thank you.


Source : https://www.dcode.fr/complex-number-conjugate
© 2019 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode
Feedback