Manuals/calci/IMCONJUGATE

IMCONJUGATE(z)

where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z} is the complex number.

Description

This function gives the conjugate of a complex number.
The complex number Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z = a+bi} , then Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle IMCONJUGATE(a+bi) = z(bar) = a-bi} and it is denoted by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{z}} or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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

if imaginary number is '0' and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z=\bar{\bar{z}} = z}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\bar{z}|=|z|} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |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.

=IMCONJUGATE("3+4i")=3+-4i =IMCONJUGATE("6-7i")=6+7i =IMCONJUGATE("2")=2+0i =IMCONJUGATE("8j")=0+-8j =IMCONJUGATE("5+0i")=5+0i