Difference between revisions of "Manuals/calci/IMAGINARY"
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==References== | ==References== | ||
| − | [http://en.wikipedia.org/wiki/Imaginary_number | + | [http://en.wikipedia.org/wiki/Imaginary_number Imaginary Number] |
Revision as of 22:34, 11 December 2013
IMAGINARY(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} is the complex 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 a+bi} .
Description
- This function gives the imaginary coefficient of a complex number.
- Imaginary number is a real number which is multiplied with 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} , 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}} .
- When 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 bi} is get adding to 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 a} , then it forms a complex number.
- Also when we are squaring 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 bi} , it will give the negative 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 {-b}^2} .
- For eg 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 (5i)^2=-25} . We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.
- A complex number is a imaginary number when the real part is zero.
Examples
IMAGINARY("2+3i")=3
IMAGINARY("4-5i")=-5
IMAGINARY("3j")=3
IMAGINARY("7")=0
| Equation | Real Part | Imaginary Part | Result(Imaginary) |
|---|---|---|---|
| =IMAGINARY("2+3i") | 2 | 3i | 3 |
| =IMAGINARY("4-5i") | 4 | -5i | -5 |
| =IMAGINARY("3j") | 0 | 3j | 3 |
| =IMAGINARY("7") | 7 | 0 | 0 |