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 z(bar) 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=z(bar) iff imaginary number is '0' and z(bar)(bar)=z
- |z(bar)|=|z| and|z|^2=z.z(bar)=z(bar).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.
Examples
- IMCONJUGATE("3+4i")=3+-4i
- IMCONJUGATE("6-7i")=6+7i
- IMCONJUGATE("2")=2+0i
- IMCONJUGATE("8j")=0+-8j
- IMCONJUGATE("5+0i")=5+0i