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.

Complex Number Conjugate - 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*!

Sponsored ads

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.

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 with respect to the abscissa axis.

Consider 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:

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

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

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, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the online Complex Number Conjugate script for offline use, for you, your company or association, see you on contact page !

conjugate,complex,number,plane,symmetry,symmetric,calculator

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

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