Difference between revisions of "Manuals/calci/COMPLEX"
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==Description== | ==Description== | ||
*COMPLEX function converts the real and imaginary coefficients into a complex number. | *COMPLEX function converts the real and imaginary coefficients into a complex number. | ||
| + | *A complex number is a combination of a real and an imaginary number. | ||
| + | *A number which is positive or negative, rational or irrational or decimals are called real numbers. | ||
| + | *An Imaginary number is a number that when squring it gives a negative result. | ||
| + | *For e.g. <math>{-4}^2 =16</math>. Because a negative times a negative is positive. | ||
*A complex number is a number is in the form <math> z = a + bi</math>, where <math>a</math> and <math>b</math> are real numbers and <math>i</math> is the imaginary unit. Where <math>i=\sqrt{-1}</math> | *A complex number is a number is in the form <math> z = a + bi</math>, where <math>a</math> and <math>b</math> are real numbers and <math>i</math> is the imaginary unit. Where <math>i=\sqrt{-1}</math> | ||
*In <math>COMPLEX(rn,in,sf)</math>, here <math>rn</math> is the real part of a complex number, <math>in</math> is the imaginary part of a complex number and <math>sf</math> is the imaginary unit of a complex number like <math>i</math> or <math>j</math>. | *In <math>COMPLEX(rn,in,sf)</math>, here <math>rn</math> is the real part of a complex number, <math>in</math> is the imaginary part of a complex number and <math>sf</math> is the imaginary unit of a complex number like <math>i</math> or <math>j</math>. | ||
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**<math>=COMPLEX(5,2)</math> gives <math>5+2i</math> | **<math>=COMPLEX(5,2)</math> gives <math>5+2i</math> | ||
**<math>=COMPLEX(5,2,"j")</math> gives <math>5+2j</math> | **<math>=COMPLEX(5,2,"j")</math> gives <math>5+2j</math> | ||
| + | |||
| + | ==ZOS Section== | ||
| + | *The syntax is to calculate COMPLEX in ZOS is <math>COMPLEX(REAL,IMAGINARY,SUFFIX)</math> | ||
| + | *<math>REAL</math> is the real part. | ||
| + | *<math>IMAGINARY</math> is the imaginary part. | ||
| + | *<math>SUFFIX</math> is imaginary unit which is either "i" or "j". | ||
| + | *E.x: COMPLEX(-1..1,10..11,"j") | ||
==Examples== | ==Examples== | ||
Revision as of 03:07, 7 April 2014
COMPLEX(rn,in,sf)
- 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 rn} is the 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 in} is the imaginary 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 sf} is the suffix for the imaginary number.
Description
- COMPLEX function converts the real and imaginary coefficients into a complex number.
- A complex number is a combination of a real and an imaginary number.
- A number which is positive or negative, rational or irrational or decimals are called real numbers.
- An Imaginary number is a number that when squring it gives a negative result.
- For e.g. 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 {-4}^2 =16} . Because a negative times a negative is positive.
- A complex number is a number is in the form 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 = a + bi} , 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 a} 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 b} are real numbers 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 i} is the imaginary unit. 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 i=\sqrt{-1}}
- 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 COMPLEX(rn,in,sf)} , here 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 rn} is the real part of a complex number, is the imaginary part of a complex number 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 sf} is the imaginary unit of a complex number like 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} or 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 j} .
- To mention 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} 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 j} , we must use the lower case only
- In a 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} real part is denoted by & imaginary part is denoted 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 Im(z)} .
- COMPLEX returns the error value, when 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 rn} 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 in} are non-numeric.
- Suffix 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 sf} should be either 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} or 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 j} , otherwise it shows error value.
- A Complex number whose real part is zero is said to be purely imaginary.
- A Complex number whose imaginary part is zero is a real number. In that cases we have to assign '0' for that part.
- 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 =COMPLEX(5,2)} gives 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 5+2i}
- 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 =COMPLEX(5,2,"j")} gives 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 5+2j}
is the imaginary part of a complex number 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 sf}
is the imaginary unit of a complex number like 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}
or 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 j}
.
& imaginary part is denoted 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 Im(z)}
.ZOS Section
- The syntax is to calculate COMPLEX in ZOS is 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 COMPLEX(REAL,IMAGINARY,SUFFIX)}
- 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 REAL} is the real part.
- 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 IMAGINARY} is the imaginary part.
- 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 SUFFIX} is imaginary unit which is either "i" or "j".
- E.x: COMPLEX(-1..1,10..11,"j")
Examples
| Complex(rn,in,sf) | rn | in | sf | RESULT |
|---|---|---|---|---|
| Complex(5,6) | 5 | 6 | 5+6i | |
| Complex(5,2,"j") | 5 | 2 | j | 5+2j |
| Complex(2,0,"i") | 2 | 0 | i | 2 |
| Complex(0,-4,i) | 0 | -4 | i | -4i |
| Complex(5,"j") | 5 | j | Error |