Manuals/calci/IMARGUMENT

IMARGUMENT(z)

• $z$ is the complex number is of the form $x+iy$
• $n$ is the order of the Bessel function and is an integer

Description

• 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 $x$ & 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 y} are the real numbers.
• 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 I} imaginary unit .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 i=\sqrt(-1)} .
• An argument of the complex number 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 z = x + iy} is any real quantity 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 \psi} 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 z = x + i y} = 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 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} .
• Where 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 = |z| = \sqrt{x^2+y^2}} and 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 \psi \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. *To change the Radian value to Degree we can use DEGREES function or we can multiply the answer with <math>\frac{180}{\pi}} .
• We can use COMPLEX function to convert real and imaginary number in to a complex number.

Examples

1. IMARGUMENT("3-2i") = -0.588002604
2. IMARGUMENT("5+6i") = 0.876058051
3. IMARGUMENT("2") = 0
4. IMARGUMENT("4i") = 1.570796327
5. DEGREES(IMARGUMENT("2+2i")) = 45

References

Bessel Function