Difference between revisions of "Manuals/calci/IMSQRT"

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<div style="font-size:30px">'''IMSQRT(z)'''</div><br/>
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<div style="font-size:30px">'''IMSQRT (ComplexNumber)'''</div><br/>
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*<math> z </math> is the complex number is of the form <math>x+iy</math>  
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*<math>ComplexNumber </math> is of the form <math>z=x+iy</math>.
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**IMSQRT(),returns the difference between two complex numbers
  
 
==Description==
 
==Description==
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*This function gives  square root of a complex number.
 
*This function gives  square root of a complex number.
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*IMSQRT(z), Where z is  the complex number is in the form of "x+iy".
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*IMSQRT(ComplexNumber), where complex number is in the form of "x+iy".
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*where x&y are the real numbers.'i' imaginary unit .<math>i=\sqrt{-1}</math>.
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*where x&y are the real numbers.<math>i</math> imaginary unit .<math>i=\sqrt{-1}</math>.
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*The square root of a complex number is defined by <math>\sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^iθ}=\sqrt{r}(cos(θ/2)+isin(θ/2)</math>
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*Consider the complex number z.
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*where r is the modulus of z. <math>r=\sqrt{x^2+y^2}</math>  
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*The square root of a complex number is defined by:
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*And θ is the argument of z. <math> θ=tan^{-1}(y/x)</math> also θ∈(-Pi(),Pi()].
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<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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*We can use COMPLEX function to convert real and imaginary number in to a complex number.
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*where <math>r</math> is the modulus of <math>z</math>. <math>r=\sqrt{x^2+y^2}</math>  
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</div></div>
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*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>.
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*We can use [[Manuals/calci/COMPLEX| COMPLEX]]  function to convert real and imaginary number in to a complex number.
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Remarks
 
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Examples
 
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<div id="8SpaceContent" align="left"><div class="ZEditBox" align="justify">'''<font face="Times New Roman">''''''''''''<font size="6"> </font>''' '''''''''</font>'''</div></div>
 
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<font size="5">Description</font>
 
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<font color="#484848"><font face="Arial, sans-serif"><font size="2">This function calculates the square root of a complex number in a + bi or a + bj text format.</font></font></font>
 
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<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify"><font size="6"> '''<font face="Arial">IMSQRT</font>'''</font></div></div>
 
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<font color="#484848"><font face="Arial, sans-serif"><font size="2">The square root of a complex number is: </font></font></font>
 
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<font color="#484848"></font>
 
  
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<font color="#484848"><font face="Arial, sans-serif"><font size="2"></font></font></font>
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==ZOS==
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*The syntax is to calculate square root of a complex number in ZOS is <math>IMSQRT(ComplexNumber)</math>.
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**<math>ComplexNumber</math> is of the form <math>z=x+iy</math>  
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*For e.g.,IMSQRT("9+10i")
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*IMSQRT(IMSUB("9+10i","-2-3i"))
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{{#ev:youtube|ofW56najtOE|280|center|Imaginary Square Root}}
  
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<font color="#484848"></font>
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==Examples==
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#=IMSQRT("2+3i")=1.67414922803554+0.895977476129838i
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#=IMSQRT("-4-5i")=1.09615788950152-2.2806933416653i
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#=IMSQRT("7")=2.6457513110645907+ⅈ0                 
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#=IMSQRT("8i")=2+2i
  
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==Related Videos==
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<font color="#484848"><font face="Arial, sans-serif"><font size="2">'''IMSQRT'''</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">(</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">'''IN'''</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">)</font></font></font>
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{{#ev:youtube|X7Fzk4ijRz8|280|center|IMSQRT}}
  
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<font color="#484848"><font face="Arial, sans-serif"><font size="2">where IN</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">   is the complex number </font></font></font>
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==See Also==
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*[[Manuals/calci/IMREAL  | IMREAL ]]
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*[[Manuals/calci/IMSUM  | IMSUM ]]
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*[[Manuals/calci/IMAGINARY  | IMAGINARY ]]
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*[[Manuals/calci/COMPLEX  | COMPLEX ]]
  
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[http://en.wikipedia.org/wiki/Binary_logarithm Binary Logarithm]
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<div align="left">[[Image:calci1.gif]]</div></div>
 
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<div id="9SpaceContent" class="zcontent" align="left"><font size="2" face="Arial">  </font>
 
  
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<font size="2" color="#484848"><font size="2" face="Arial">Let's see an example</font></font>
 
  
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<font size="2" color="#484848"><font size="2" face="Arial">I.e =IMSQRT(“2+i”) is 1.4553+0.34356i</font></font>
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*[[Z_API_Functions | List of Main Z Functions]]
  
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*[[ Z3 |   Z3 home ]]
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<div id="12SpaceContent" class="zcontent" align="left"><div>[[Image:equation%202sqrt.jpg|100%px|http://store.zcubes.com/33975CA25A304262905E768B19753F5D/Uploaded/equation%202sqrt.jpg]]</div></div>
 
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Latest revision as of 15:05, 18 July 2018

IMSQRT (ComplexNumber)


  • is of the form .
    • IMSQRT(),returns the difference between two complex numbers

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"))
Imaginary Square Root

Examples

  1. =IMSQRT("2+3i")=1.67414922803554+0.895977476129838i
  2. =IMSQRT("-4-5i")=1.09615788950152-2.2806933416653i
  3. =IMSQRT("7")=2.6457513110645907+ⅈ0
  4. =IMSQRT("8i")=2+2i

Related Videos

IMSQRT

See Also


References

Binary Logarithm


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