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 $IMCONJUGATE(a+bi)=z(bar)=a-bi$ and it is denoted by Failed to parse (syntax error): {\displaystyle \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=z(bar) iff imaginary number is '0' and z(bar)(bar)=z
2. |z(bar)|=|z| and|z|^2=z.z(bar)=z(bar).z
3. Real part (a)=z+z(bar)/2
4. Imaginary part(b)=z-z(bar)/2i.We can use COMPLEX function to convert the real and imginary coefficients to a complex number.

Examples

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

See Also

• COMPLEX
• IMREAL
• IMAGINARY

References

Exponential function