Manuals/calci/IMARGUMENT

IMARGUMENT(Complexnumber)

• $Complexnumber$ is of the form $z=x+iy$.

Description

• This function gives the principal value of an argument of a complex-valued expression $z$.
• i.e The angle from the positive axis to the line segment is called the Argument of a complex number.
• In this function angle value is in Radians.
• Here $IMARGUMENT(Complexnumber)$, Where Complexnumber in the form of $z=x+iy$. i.e $x$ & $y$ are the real numbers.
• $I$ imaginary unit .$i={\sqrt {-1}}$.
• An argument of the complex number $z=x+iy$ is any real quantity $\phi$ such that $z=x+iy$ = $rcos(\phi )+irsin(\phi )$ for some positive real number $r$.
• Where $r=|z|={\sqrt {x^{2}+y^{2}}}$ and $\phi \in (-\pi ,\pi ]$.
• The argument of a complex number is calculated by $arg(z)=tan^{-1}({\frac {y}{x}})=\theta$ in Radians.
• To change the Radian value to Degree we can use DEGREES function or we can multiply the answer with ${\frac {180}{\pi }}$.
• We can use COMPLEX function to convert real and imaginary number in to a complex number.

ZOS Section

• The syntax is to calculate argument of a complex number in ZOS is $IMARGUMENT(Complexnumber)$.
  • $Complexnumber$ is of the form $z=x+iy$.
• For e.g.,IMARGUMENT("6.72+1.5i")

Imargument

Examples

1. IMARGUMENT("3-2i") = -0.5880026035475675
2. IMARGUMENT("5+6i") = 0.8760580505981934
3. IMARGUMENT("2") = 0
4. IMARGUMENT("4i") = 1.5707963267948966
5. DEGREES(IMARGUMENT("2+2i")) = 45

See Also

• IMAGINARY
• IMREAL
• IMSUM

References

• Complex Argument