Difference between revisions of "Manuals/calci/IMARGUMENT"
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*<math>n</math> is the order of the Bessel function and is an integer | *<math>n</math> is the order of the Bessel function and is an integer | ||
==Description== | ==Description== | ||
| − | *This function gives the principal value of the argument of the complex-valued expression z. i.e | + | *This function gives the principal value of the argument of the complex-valued expression <math>z</math>. |
| − | + | * 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 | + | *In this function angle value is in Radians. |
| − | *Here IMARGUMENT(z), Where z is the complex number in the form of | + | *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 z = x + iy is any real quantity | + | *An argument of the complex number <math>z = x + iy</math> is any real quantity <math>\psi</math> such that <math>z = x + i y</math> = <math>r cosφ + i r sinφ</math> for some positive real number <math>r</math>. |
| − | *Where r=|z|=sqrt | + | *Where <math>r = |z| = \sqrt{x^2+y^2}</math> and <math>\psi \in [(-\Pi(),\Pi()]<math>. |
| − | *The argument of a complex number is calculated by arg(z)= tan^-1(y | + | *The argument of a complex number is calculated by <math>arg(z)= tan^{-1}(\frac{y}{x}) =\theta<math> in Radians. |
| − | *To change the | + | *To change the Radian value to Degree we can use DEGREES function or we can multiply the answer with <math>\frac{180}{\pi}</math>. |
| − | *We can use COMPLEX function to convert | + | *We can use COMPLEX function to convert real and imaginary number in to a complex number. |
==Examples== | ==Examples== | ||
| − | #IMARGUMENT("3-2i")=-0.588002604 | + | #IMARGUMENT("3-2i") = -0.588002604 |
| − | #IMARGUMENT("5+6i")=0.876058051 | + | #IMARGUMENT("5+6i") = 0.876058051 |
| − | #IMARGUMENT("2")=0 | + | #IMARGUMENT("2") = 0 |
| − | #IMARGUMENT("4i")=1.570796327 | + | #IMARGUMENT("4i") = 1.570796327 |
| − | #DEGREES(IMARGUMENT("2+2i"))=45 | + | #DEGREES(IMARGUMENT("2+2i")) = 45 |
| − | |||
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==References== | ==References== | ||
[http://en.wikipedia.org/wiki/Bessel_function Bessel Function] | [http://en.wikipedia.org/wiki/Bessel_function Bessel Function] | ||
Revision as of 00:51, 16 December 2013
IMARGUMENT(z)
- is the complex number is of the form
- is the order of the Bessel function and is an integer
is the complex number is of the form 
is the order of the Bessel function and is an integerDescription
- This function gives the principal value of the argument of the complex-valued expression .
- 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 is the complex number in the form of . i.e & are the real numbers.
- imaginary unit ..
- An argument of the complex number is any real quantity such that = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r cosφ + i r sinφ} for some positive real number .
- Where and .
- We can use COMPLEX function to convert real and imaginary number in to a complex number.
& 
are the real numbers.
imaginary unit .
.
is any real quantity 
such that 
.
and ![{\displaystyle \psi \in [(-\Pi (),\Pi ()]<math>.*Theargumentofacomplexnumberiscalculatedby<math>arg(z)=tan^{-1}({\frac {y}{x}})=\theta <math>inRadians.*TochangetheRadianvaluetoDegreewecanuseDEGREESfunctionorwecanmultiplytheanswerwith<math>{\frac {180}{\pi }}}](https://wikimedia.org/api/rest_v1/media/math/render/png/08c6e7a9cea25f7c6bf03a65e194cf7372717e61)
.Examples
- IMARGUMENT("3-2i") = -0.588002604
- IMARGUMENT("5+6i") = 0.876058051
- IMARGUMENT("2") = 0
- IMARGUMENT("4i") = 1.570796327
- DEGREES(IMARGUMENT("2+2i")) = 45