Difference between revisions of "Manuals/calci/IMSQRT"

Latest revision as of 15:05, 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} .
- 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.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"))

Imaginary Square Root

Examples

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

References

Binary Logarithm

List of Main Z Functions

Z3 home

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''IMSQRT(z)'''</div><br/>
+<div style="font-size:30px">'''IMSQRT (ComplexNumber)'''</div><br/>
-*<math> z </math> is the complex number is of the form <math>x+iy</math>
+*<math>ComplexNumber </math> is of the form <math>z=x+iy</math>.
+**IMSQRT(),returns the difference between two complex numbers
 ==Description==
 *This function gives  square root of a complex number.
-*IMSQRT(z), where z  is  the complex number is in the form of "x+iy".
+*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>.
+*Consider the complex number z.
 *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{θ}{2})+isin(\frac{θ}{2})</math>
+<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>
-*And <math>\theta</math> is the argument of <math>z</math>. <math> θ=tan^{-1}(y/x)</math> also <math>θ∈(-pi(),pi()]</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 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==
+*The syntax is to calculate square root of a complex number in ZOS is <math>IMSQRT(ComplexNumber)</math>.
+**<math>ComplexNumber</math> is of the form <math>z=x+iy</math>
+*For e.g.,IMSQRT("9+10i")
+*IMSQRT(IMSUB("9+10i","-2-3i"))
+{{#ev:youtube|ofW56najtOE|280|center|Imaginary Square Root}}
 ==Examples==
 #=IMSQRT("2+3i")=1.67414922803554+0.895977476129838i
 #=IMSQRT("-4-5i")=1.09615788950152-2.2806933416653i
-#=IMSQRT("7")=2.64575131106459
+#=IMSQRT("7")=2.6457513110645907+ⅈ0
 #=IMSQRT("8i")=2+2i
+==Related Videos==
+{{#ev:youtube|X7Fzk4ijRz8|280|center|IMSQRT}}
 ==See Also==
@@ Line 30: / Line 40: @@
 ==References==
 [http://en.wikipedia.org/wiki/Binary_logarithm  Binary Logarithm]
+*[[Z_API_Functions | List of Main Z Functions]]
+*[[ Z3 |   Z3 home ]]