Difference between revisions of "Manuals/calci/IMCONJUGATE"

Revision as of 05:44, 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

$z={\bar {z}}$ if imaginary number is '0' and $z={\bar {\bar {z}}}=z$
$|{\bar {z}}|=|z|$ and $|z|^{2}=z.{\bar {z}}={\bar {z}}.z$
$Realpart(a)={\frac {z+{\bar {z}}}{2}}$
$Imaginarypart(b)={\frac {z-{\bar {z}}}{2i}}$ .We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.

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

@@ Line 9: / Line 9: @@
 #<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>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>.We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.
+#<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==