Manuals/calci/IMCONJUGATE

IMCONJUGATE(z)

• where $z$ is the complex number.

Description

• This function gives the conjugate of a complex number.
• The complex number $z=a+bi$, then: $IMCONJUGATE(a+bi)={\bar {z}}=a-bi$ 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

1. $z={\bar {z}}$ 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 \bar{\bar{z}} = z}
2. 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}
3. 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 Real part (a)=\frac{z+\bar z}{2}}
4. 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 Imaginary part (b)=\frac{z-\bar z}{2i}} .

We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.

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

See Also

• COMPLEX
• IMREAL
• IMAGINARY

References

Exponential function