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 | + | #<math>Real part (a)=\frac{z+\bar z}{2}</math> |
− | #<math>Imaginary part (b)=\frac{z-\bar | + | #<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 05:44, 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 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
- if imaginary number is '0' and
- and
- .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 |