Difference between revisions of "Manuals/calci/IMCONJUGATE"
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<div style="font-size:30px">'''IMCONJUGATE(z)'''</div><br/> | <div style="font-size:30px">'''IMCONJUGATE(z)'''</div><br/> | ||
− | *where | + | *where <math>z</math> is the complex number. |
==Description== | ==Description== | ||
*This function gives the conjugate of a complex number. | *This function gives the conjugate of a complex number. | ||
− | *The complex number z=a+bi, then IMCONJUGATE(a+bi)=z(bar)=a-bi and it is denoted by | + | *The complex number <math>z = a+bi</math>, then <math>IMCONJUGATE(a+bi) = z(bar) = a-bi</math> and it is denoted by <math>\bar_z</math> or <math>z^*</math>. |
*So complex number and complex conjugate both also having same real number and imaginary number with | *So complex number and complex conjugate both also having same real number and imaginary number with | ||
the equal magnitude and opposite sign of a imaginary number.Also | the equal magnitude and opposite sign of a imaginary number.Also |
Revision as of 03:52, 25 November 2013
IMCONJUGATE(z)
- where is the complex number.
Description
- This function gives the conjugate of a complex number.
- The complex number , then and it is denoted by Failed to parse (syntax error): {\displaystyle \bar_z} or .
- So complex number and complex conjugate both also having same real number and imaginary number with
the equal magnitude and opposite sign of a imaginary number.Also
- z=z(bar) iff imaginary number is '0' and z(bar)(bar)=z
- |z(bar)|=|z| and|z|^2=z.z(bar)=z(bar).z
- Real part (a)=z+z(bar)/2
- Imaginary part(b)=z-z(bar)/2i.We can use COMPLEX function to convert the real and imginary coefficients to a complex number.
Examples
- IMCONJUGATE("3+4i")=3+-4i
- IMCONJUGATE("6-7i")=6+7i
- IMCONJUGATE("2")=2+0i
- IMCONJUGATE("8j")=0+-8j
- IMCONJUGATE("5+0i")=5+0i