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. |
| + | |||
==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>z=\bar{z}</math> if imaginary number is '0' and <math>\bar{\bar{z}} = z</math> | ||
| Line 11: | Line 14: | ||
#<math>Real part (a)=\frac{z+\bar z}{2}</math> | #<math>Real part (a)=\frac{z+\bar z}{2}</math> | ||
#<math>Imaginary part (b)=\frac{z-\bar z}{2i}</math>. | #<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. | + | *We can use [[Manuals/calci/COMPLEX | COMPLEX ]] function to convert the real and imaginary coefficients to a complex number. |
| + | |||
| + | ==ZOS Section== | ||
| + | *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") | ||
==Examples== | ==Examples== | ||
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==See Also== | ==See Also== | ||
| + | |||
*[[Manuals/calci/COMPLEX | COMPLEX ]] | *[[Manuals/calci/COMPLEX | COMPLEX ]] | ||
*[[Manuals/calci/IMREAL | IMREAL ]] | *[[Manuals/calci/IMREAL | IMREAL ]] | ||
Revision as of 01:24, 24 April 2014
IMCONJUGATE(ComplexNumber)
- is of the form a+bi.
is of the form a+bi.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
, then: 
and it is denoted by 
or 
.the equal magnitude and opposite sign of a imaginary number.
- The properties of a Complex Conjugate are:
- if imaginary number is '0' and
- and
- .
if imaginary number is '0' and 
and 
.- We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.
ZOS Section
- 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 |