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>. |
+ | **IMSQRT(),returns the difference between two complex numbers | ||
==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{ | + | <math>\sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^{i\theta}}=\sqrt{{r}(cos(\frac{\theta}{2})+isin(\frac{\theta}{2})}</math> |
*where <math>r</math> is the modulus of <math>z</math>. <math>r=\sqrt{x^2+y^2}</math> | *where <math>r</math> is the modulus of <math>z</math>. <math>r=\sqrt{x^2+y^2}</math> | ||
− | *And <math>\theta</math> is the argument of <math>z</math>. <math> | + | *And <math>\theta</math> is the argument of <math>z</math>. <math> \theta=tan^{-1}(y/x)</math> also <math>\theta \isin (-\pi,\pi]</math>. |
*We can use [[Manuals/calci/COMPLEX| COMPLEX]] function to convert real and imaginary number in to a complex number. | *We can use [[Manuals/calci/COMPLEX| COMPLEX]] function to convert real and imaginary number in to a complex number. | ||
==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")) | ||
Line 22: | Line 24: | ||
#=IMSQRT("2+3i")=1.67414922803554+0.895977476129838i | #=IMSQRT("2+3i")=1.67414922803554+0.895977476129838i | ||
#=IMSQRT("-4-5i")=1.09615788950152-2.2806933416653i | #=IMSQRT("-4-5i")=1.09615788950152-2.2806933416653i | ||
− | #=IMSQRT("7")=2. | + | #=IMSQRT("7")=2.6457513110645907+ⅈ0 |
#=IMSQRT("8i")=2+2i | #=IMSQRT("8i")=2+2i | ||
Line 38: | Line 40: | ||
==References== | ==References== | ||
[http://en.wikipedia.org/wiki/Binary_logarithm Binary Logarithm] | [http://en.wikipedia.org/wiki/Binary_logarithm Binary Logarithm] | ||
+ | |||
+ | |||
+ | |||
+ | *[[Z_API_Functions | List of Main Z Functions]] | ||
+ | |||
+ | *[[ Z3 | Z3 home ]] |
Latest revision as of 16:05, 18 July 2018
IMSQRT (ComplexNumber)
- IMSQRT(),returns the difference between two complex numbers
is of the form .
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. imaginary unit . .
- Consider the complex number z.
- The square root of a complex number is defined by:
- where is the modulus of .
- And is the argument of . also .
- 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
- is of the form
.
- 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