Difference between revisions of "Manuals/calci/IMSQRT"
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| − | <div style="font-size:30px">'''IMSQRT( | + | <div style="font-size:30px">'''IMSQRT (ComplexNumber)'''</div><br/> |
| − | *<math> | + | *<math>ComplexNumber </math> is of the form <math>z=x+iy</math> |
==Description== | ==Description== | ||
*This function gives square root of a complex number. | *This function gives square root of a complex number. | ||
| − | *IMSQRT( | + | *IMSQRT(ComplexNumber), where complex number is in the form of "x+iy". |
*where x&y are the real numbers.<math>i</math> imaginary unit .<math>i=\sqrt{-1}</math>. | *where x&y are the real numbers.<math>i</math> imaginary unit .<math>i=\sqrt{-1}</math>. | ||
| + | *Consider the complex number z. | ||
*The square root of a complex number is defined by: | *The square root of a complex number is defined by: | ||
<math>\sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^{i\theta}}=\sqrt{{r}(cos(\frac{\theta}{2})+isin(\frac{\theta}{2})}</math> | <math>\sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^{i\theta}}=\sqrt{{r}(cos(\frac{\theta}{2})+isin(\frac{\theta}{2})}</math> | ||
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==ZOS== | ==ZOS== | ||
| − | *The syntax is to calculate square root of a complex number in ZOS is <math>IMSQRT( | + | *The syntax is to calculate square root of a complex number in ZOS is <math>IMSQRT(ComplexNumber)</math>. |
| − | **<math> | + | **<math>ComplexNumber</math> is of the form <math>z=x+iy</math> |
*For e.g.,IMSQRT("9+10i") | *For e.g.,IMSQRT("9+10i") | ||
*IMSQRT(IMSUB("9+10i","-2-3i")) | *IMSQRT(IMSUB("9+10i","-2-3i")) | ||
Revision as of 14:55, 18 July 2018
IMSQRT (ComplexNumber)
- 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 ComplexNumber } is of 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=x+iy}
Description
- This function gives square root of a complex number.
- IMSQRT(ComplexNumber), where complex number is in the form of "x+iy".
- where x&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}} .
- Consider the complex number z.
- The square root of a complex number is defined 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 \sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^{i\theta}}=\sqrt{{r}(cos(\frac{\theta}{2})+isin(\frac{\theta}{2})}}
- 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} is the modulus of 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} . 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=\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 \theta} is the argument of 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} . 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 \theta=tan^{-1}(y/x)} also 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 \theta \isin (-\pi,\pi]} .
- We can use COMPLEX function to convert real and imaginary number in to a complex number.
ZOS
- The syntax is to calculate square root of a complex number 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 IMSQRT(ComplexNumber)}
.
- 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 ComplexNumber} is of 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=x+iy}
- For e.g.,IMSQRT("9+10i")
- IMSQRT(IMSUB("9+10i","-2-3i"))
Examples
- =IMSQRT("2+3i")=1.67414922803554+0.895977476129838i
- =IMSQRT("-4-5i")=1.09615788950152-2.2806933416653i
- =IMSQRT("7")=2.6457513110645907+ⅈ0
- =IMSQRT("8i")=2+2i
Related Videos
See Also
References