Difference between revisions of "Manuals/calci/IMCONJUGATE"
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(Created page with "<div id="7SpaceContent" class="zcontent" align="left"> <font color="#000000"><font face="Arial, sans-serif"><font size="2">The conjugate of a complex number is: </font></fo...") |
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| − | <div | + | <div style="font-size:30px">'''IMCONJUGATE(z)'''</div><br/> |
| + | *where 'z' is the complex number. | ||
| + | ==Description== | ||
| + | *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 z(bar) or z^*. | ||
| + | *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 | ||
| − | + | 1. z=z(bar) iff imaginary number is '0' and z(bar)(bar)=z | |
| + | 2.|z(bar)|=|z| and|z|^2=z.z(bar)=z(bar).z | ||
| + | 3. Real part (a)=z+z(bar)/2 | ||
| + | 4. 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 | ||
| − | + | ==See Also== | |
| − | + | *[[Manuals/calci/COMPLEX | COMPLEX ]] | |
| − | + | *[[Manuals/calci/IMREAL | IMREAL ]] | |
| + | *[[Manuals/calci/IMAGINARY | IMAGINARY ]] | ||
| − | + | ==References== | |
| − | + | [http://en.wikipedia.org/wiki/Exponential_function| Exponential function] | |
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Revision as of 06:20, 23 November 2013
IMCONJUGATE(z)
- where 'z' is the complex number.
Description
- 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 z(bar) or z^*.
- 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
1. z=z(bar) iff imaginary number is '0' and z(bar)(bar)=z 2.|z(bar)|=|z| and|z|^2=z.z(bar)=z(bar).z 3. Real part (a)=z+z(bar)/2 4. 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