Difference between revisions of "Manuals/calci/IMEXP"
Jump to navigation
Jump to search
| Line 1: | Line 1: | ||
<div style="font-size:30px">'''IMEXP(z)'''</div><br/> | <div style="font-size:30px">'''IMEXP(z)'''</div><br/> | ||
| − | *where | + | *where <math>z</math> is the complex number. |
==Description== | ==Description== | ||
*This function gives the exponential of a complex number. | *This function gives the exponential of a complex number. | ||
| − | * | + | *In <math>IMEXP(z)</math>, <math>z<math> is the complex number of the form <math>z=x+iy</math>, <math>x</math>&<math>y</math> are real numbers & <math>i</math> is the imaginary unit. <math>i=sqrt{-1}</math>. |
| − | *Euler's formula states that e^ix=cosx+isinx, for any real number x and e is the base of the natural logarithm. | + | *Euler's formula states that <math>e^{ix}= cosx+isinx<math>, for any real number <math>x<math> and <math>e</math> is the base of the natural logarithm. |
| − | *The approximate value of the constant e=2.718281828459045 and it is equal to e^1. So the exponential of a complex number is : IMEXP(z)=e^z=e^(x+iy)=e^x.e^iy=e^x.(cosy+isiny) | + | *The approximate value of the constant e=2.718281828459045 and it is equal to <math>e^1</math>. So the exponential of a complex number is : <math>IMEXP(z)=e^z=e^(x+iy)=e^x.e^iy=e^x.(cosy+isiny)=e^x.cosy+ie^x.siny</math>. |
| − | + | *When imaginary part is '0', it will give the exponent value of the real number. *i.e.IMEXP(z)=EXP(z) when imaginary number (iy) is '0'. | |
| − | *We can use COMPLEX function to convert the real and | + | *We can use COMPLEX function to convert the real and imaginary coefficients to a complex number. |
==Examples== | ==Examples== | ||
Revision as of 04:58, 25 November 2013
IMEXP(z)
- 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 z} is the complex number.
Description
- This function gives the exponential of a complex number.
- In 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 IMEXP(z)} , 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<math> is the complex number of the form <math>z=x+iy} , 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 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 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} is the 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}} .
- Euler's formula states 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 e^{ix}= cosx+isinx<math>, for any real number <math>x<math> and <math>e} is the base of the natural logarithm.
- The approximate value of the constant e=2.718281828459045 and it is equal to 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 e^1} . So the exponential of a complex number is : Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle IMEXP(z)=e^{z}=e^{(}x+iy)=e^{x}.e^{i}y=e^{x}.(cosy+isiny)=e^{x}.cosy+ie^{x}.siny} .
- When imaginary part is '0', it will give the exponent value of the real number. *i.e.IMEXP(z)=EXP(z) when imaginary number (iy) is '0'.
- We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.
Examples
- IMEXP("2+3i")=-7.315110094901102+1.0427436562359i
- IMEXP("4-5i")=15.4874305606508+52.355491418482i
- IMEXP("6")=403.428793492735
- IMEXP("2i")=-0.416146836547142+0.909297426825682i
- IMEXP("0")=1 andIMEXP("0i")=1