Difference between revisions of "Manuals/calci/IMCONJUGATE"
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#<math>z=\bar{z}</math> if imaginary number is '0' and <math>z=\bar{\bar{z}} = z</math> | #<math>z=\bar{z}</math> if imaginary number is '0' and <math>z=\bar{\bar{z}} = z</math> | ||
#<math>|\bar{z}|=|z|</math> and <math>|z|^2 = z.\bar{z} = \bar{z}.z</math> | #<math>|\bar{z}|=|z|</math> and <math>|z|^2 = z.\bar{z} = \bar{z}.z</math> | ||
| − | #<math>Real part (a)=\frac{z+\bar(z | + | #<math>Real part (a)=\frac{z+\bar(z)}{2}</math> |
| − | #Imaginary part (b)=z-z | + | #<math>Imaginary part (b)=\frac{z-\bar(z)}{2i}</math>.We can use COMPLEX function to convert the real and imaginary coefficients to a complex number. |
==Examples== | ==Examples== | ||
Revision as of 04:43, 25 November 2013
IMCONJUGATE(z)
- where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z} is the complex number.
Description
- This function gives the conjugate of a complex number.
- The complex number Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z = a+bi} , then Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle IMCONJUGATE(a+bi) = z(bar) = a-bi} and it is denoted by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{z}} or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z=\bar{z}} if imaginary number is '0' and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z=\bar{\bar{z}} = z}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\bar{z}|=|z|} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |z|^2 = z.\bar{z} = \bar{z}.z}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Real part (a)=\frac{z+\bar(z)}{2}}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Imaginary part (b)=\frac{z-\bar(z)}{2i}} .We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.
Examples
| Equation | a | bi | Result | Result |
|---|---|---|---|---|
| =IMCONJUGATE("3+4i") | 3 | 4i | 3+4i | 3-4i |
| =IMCONJUGATE("6-7i") | 6 | -7i | 6+7i | |
| =IMCONJUGATE("8j") | 0 | 8j | 0+8j | 0-8j |
| =IMCONJUGATE("2") | 2 | 0 | 2+0i | |
| =IMCONJUGATE("5+0i") | 5 | 0i | 5+0i |