Difference between revisions of "Manuals/calci/IMARGUMENT"

Revision as of 22:31, 17 December 2013

IMARGUMENT(z)

This function gives the principal value of the argument of the 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(z), Where $z$ is the complex number in the form of $x+iy$ . 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.

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 *Here IMARGUMENT(z), Where <math>z</math> is the complex number in the form of <math>x+iy</math>. i.e  <math>x</math> & <math>y</math> are the real numbers.
 *<math>I</math> imaginary unit .<math>i=\sqrt{-1}</math>.
-*An argument of the complex number <math>z = x + iy</math> is any real quantity <math>\phi</math> such that <math>z = x + i y</math> = <math>r cos(\psi) + i r sin(\phi)</math> for some positive real number <math>r</math>.
+*An argument of the complex number <math>z = x + iy</math> is any real quantity <math>\phi</math> such that <math>z = x + i y</math> = <math>r cos(\phi) + i r sin(\phi)</math> for some positive real number <math>r</math>.
 *Where <math>r = |z| = \sqrt{x^2+y^2}</math> and <math>\phi \in (-\pi,\pi]</math>.
 *The argument of a complex number is calculated by <math>arg(z)= tan^{-1}(\frac{y}{x}) =\theta</math> in Radians.