Difference between revisions of "Manuals/calci/IMCONJUGATE"

Revision as of 04:02, 25 November 2013

IMCONJUGATE(z)

This function gives the conjugate of a complex number.
The complex number $z=a+bi$ , then $IMCONJUGATE(a+bi)=z(bar)=a-bi$ and it is denoted by ${\bar {z}}$ or $z^{*}$ .
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 (syntax error): {\displaystyle z=/bar{x)} if imaginary number is '0' and $z=/bar{/bar{x}}=z$
$|/bar{z}|=|z|$ and $|z|^{2}=z.{\bar {z}}={\bar {z}}.z$
Real part (a)=z+z(bar)/2
Imaginary part(b)=z-z(bar)/2i.We can use COMPLEX function to convert the real and imginary coefficients to a complex number.

@@ Line 3: / Line 3: @@
 ==Description==
 *This function gives the conjugate of a complex number.
-*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>.
+*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>.
 *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
-#z=z(bar) iff imaginary number is '0' and z(bar)(bar)=z
+#<math>z=/bar{x)</math> if imaginary number is '0' and <math>z=/bar{/bar{x}} = z</math>
-#|z(bar)|=|z| and|z|^2=z.z(bar)=z(bar).z
+#<math>|/bar{z}|=|z|</math>  and <math>|z|^2 = z.\bar{z} = \bar{z}.z</math>
 #Real part (a)=z+z(bar)/2
 #Imaginary part(b)=z-z(bar)/2i.We can use COMPLEX function to convert the real and imginary coefficients to a complex number.