Difference between revisions of "Manuals/calci/IMCONJUGATE"

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<div style="font-size:30px">'''IMCONJUGATE(z)'''</div><br/>
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<div style="font-size:30px">'''IMCONJUGATE(ComplexNumber)'''</div><br/>
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*where <math>z</math> is the complex number.
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*<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.  
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*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>.  
+
*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  
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the equal magnitude and opposite sign of a imaginary number.Also
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the equal magnitude and opposite sign of a imaginary number.
 +
*The properties of a Complex Conjugate are:
  
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#<math>z=\bar{x}</math> if imaginary number is '0' and <math>z=\bar{\bar{x}} = z</math>
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#<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>|\bar{z}|=|z|</math>  and <math>|z|^2 = z.\bar{z} = \bar{z}.z</math>
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#Real part (a)=z+z(bar)/2
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#<math>Real part (a)=\frac{z+\bar z}{2}</math>
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#Imaginary part(b)=z-z(bar)/2i.We can use COMPLEX function to convert the real and imginary coefficients to a complex number.
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#<math>Imaginary part (b)=\frac{z-\bar z}{2i}</math>.
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*We can use [[Manuals/calci/COMPLEX | COMPLEX ]] function to convert the real and imaginary coefficients to a complex number.
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 +
==ZOS==
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*The Syntax is to calculate IMCONJUGATE in ZOS is <math>IMCONJUGATE(Complexnumber)</math>.
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**<math>ComplexNumber</math> is of the form a+bi.
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*For e.g.,IMCONJUGATE("-10+8.25i")
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{{#ev:youtube|rwCcfUGpk9Q|280|center|IMConjugate}}
  
 
==Examples==
 
==Examples==
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=IMCONJUGATE("3+4i")=3+-4i
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=IMCONJUGATE("6-7i")=6+7i
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{| id="TABLE3" class="SpreadSheet blue"
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=IMCONJUGATE("2")=2+0i
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|- class="even"
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=IMCONJUGATE("8j")=0+-8j
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!Equation
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=IMCONJUGATE("5+0i")=5+0i
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! a
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! bi
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! Conjugate
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|- class="odd"
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|=IMCONJUGATE("3+4i")
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| 3
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| 4i
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| 3-4i
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|- class="even"
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| =IMCONJUGATE("6-7i")
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| 6
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| -7i
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| 6+7i  
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|- class="odd"
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| =IMCONJUGATE("8j")
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| 0                       
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| 8j
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| 0-8j
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|- class="even"
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| =IMCONJUGATE("2")
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| 2                       
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| 0
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| 2+0i
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|- class="odd"
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| =IMCONJUGATE("5+0i")
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| 5                       
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| 0i
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| 5+0i
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|}
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 +
==Related Videos==
 +
 
 +
{{#ev:youtube|BZxZ_eEuJBM|280|center|Complex Conjugates}}
  
 
==See Also==
 
==See Also==
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*[[Manuals/calci/COMPLEX  | COMPLEX ]]
 
*[[Manuals/calci/COMPLEX  | COMPLEX ]]
 
*[[Manuals/calci/IMREAL  | IMREAL ]]
 
*[[Manuals/calci/IMREAL  | IMREAL ]]
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==References==
 
==References==
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[http://en.wikipedia.org/wiki/Exponential_function| Exponential function]
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[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:
  1. if imaginary number is '0' and
  2. and
  4. .
  • 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")
IMConjugate

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

Complex Conjugates

See Also

References

Complex Conjugate


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