Difference between revisions of "Manuals/calci/IMCONJUGATE"
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− | <div style="font-size:30px">'''IMCONJUGATE( | + | <div style="font-size:30px">'''IMCONJUGATE(ComplexNumber)'''</div><br/> |
− | * | + | *<math>ComplexNumber</math> is of the form a+bi. |
+ | **IMCONJUGATE(), returns the complex conjugate of a complex number | ||
+ | |||
==Description== | ==Description== | ||
+ | |||
*This function gives the conjugate of a complex number. | *This function gives the conjugate of a complex number. | ||
− | * | + | *Let the complex number be <math>z = a+bi</math>, then: <math>IMCONJUGATE(a+bi) = \bar{z} = 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. | + | the equal magnitude and opposite sign of a imaginary number. |
+ | *The properties of a Complex Conjugate are: | ||
+ | |||
+ | #<math>z=\bar{z}</math> if imaginary number is '0' and <math>\bar{\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}{2}</math> | ||
+ | #<math>Imaginary part (b)=\frac{z-\bar z}{2i}</math>. | ||
+ | *We can use [[Manuals/calci/COMPLEX | COMPLEX ]] function to convert the real and imaginary coefficients to a complex number. | ||
− | + | ==ZOS== | |
− | + | *The Syntax is to calculate IMCONJUGATE in ZOS is <math>IMCONJUGATE(Complexnumber)</math>. | |
− | + | **<math>ComplexNumber</math> is of the form a+bi. | |
− | # | + | *For e.g.,IMCONJUGATE("-10+8.25i") |
+ | {{#ev:youtube|rwCcfUGpk9Q|280|center|IMConjugate}} | ||
==Examples== | ==Examples== | ||
− | + | ||
− | + | {| id="TABLE3" class="SpreadSheet blue" | |
− | + | |- class="even" | |
− | + | !Equation | |
− | + | ! a | |
+ | ! bi | ||
+ | ! Conjugate | ||
+ | |- class="odd" | ||
+ | |=IMCONJUGATE("3+4i") | ||
+ | | 3 | ||
+ | | 4i | ||
+ | | 3-4i | ||
+ | |- class="even" | ||
+ | | =IMCONJUGATE("6-7i") | ||
+ | | 6 | ||
+ | | -7i | ||
+ | | 6+7i | ||
+ | |- class="odd" | ||
+ | | =IMCONJUGATE("8j") | ||
+ | | 0 | ||
+ | | 8j | ||
+ | | 0-8j | ||
+ | |- class="even" | ||
+ | | =IMCONJUGATE("2") | ||
+ | | 2 | ||
+ | | 0 | ||
+ | | 2+0i | ||
+ | |- class="odd" | ||
+ | | =IMCONJUGATE("5+0i") | ||
+ | | 5 | ||
+ | | 0i | ||
+ | | 5+0i | ||
+ | |} | ||
+ | |||
+ | ==Related Videos== | ||
+ | |||
+ | {{#ev:youtube|BZxZ_eEuJBM|280|center|Complex Conjugates}} | ||
==See Also== | ==See Also== | ||
+ | |||
*[[Manuals/calci/COMPLEX | COMPLEX ]] | *[[Manuals/calci/COMPLEX | COMPLEX ]] | ||
*[[Manuals/calci/IMREAL | IMREAL ]] | *[[Manuals/calci/IMREAL | IMREAL ]] | ||
Line 25: | Line 69: | ||
==References== | ==References== | ||
− | [http://en.wikipedia.org/wiki/ | + | [http://en.wikipedia.org/wiki/Complex_conjugate Complex Conjugate] |
+ | |||
+ | |||
+ | |||
+ | *[[Z_API_Functions | List of Main Z Functions]] | ||
+ | |||
+ | *[[ Z3 | Z3 home ]] |
Latest revision as of 18:38, 13 July 2018
IMCONJUGATE(ComplexNumber)
- is of the form a+bi.
- IMCONJUGATE(), returns the complex conjugate of a complex number
Description
- This function gives the conjugate of a complex number.
- Let the complex number be , 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.
- The properties of a Complex Conjugate are:
- if imaginary number is '0' and
- and
- .
- We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.
ZOS
- The Syntax is to calculate IMCONJUGATE in ZOS is .
- is of the form a+bi.
- For e.g.,IMCONJUGATE("-10+8.25i")
Examples
Equation | a | bi | Conjugate |
---|---|---|---|
=IMCONJUGATE("3+4i") | 3 | 4i | 3-4i |
=IMCONJUGATE("6-7i") | 6 | -7i | 6+7i |
=IMCONJUGATE("8j") | 0 | 8j | 0-8j |
=IMCONJUGATE("2") | 2 | 0 | 2+0i |
=IMCONJUGATE("5+0i") | 5 | 0i | 5+0i |
Related Videos
See Also
References