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 $x$ & $y$ 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 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 cos(\phi) + i r sin(\phi)} 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 \phi \in (-\pi,\pi]} .
• The argument of a complex number is calculated by 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 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 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 \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

==See Also

• IMAGINARY
• IMREAL
• IMSUM