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 $z={\bar {\bar {z}}}=z$
2. $|{\bar {z}}|=|z|$ and $|z|^{2}=z.{\bar {z}}={\bar {z}}.z$
3. $Realpart(a)={\frac {z+{\bar {z}}}{2}}$
4. $Imaginarypart(b)={\frac {z-{\bar {z}}}{2i}}$.

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

Examples

Equation	a	bi	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

See Also

• COMPLEX
• IMREAL
• IMAGINARY

References

Exponential function