Difference between revisions of "Manuals/calci/IMSQRT"
Jump to navigation
Jump to search
| Line 8: | Line 8: | ||
*IMSQRT(z), Where z is the complex number is in the form of "x+iy". | *IMSQRT(z), Where z is the complex number is in the form of "x+iy". | ||
*where x&y are the real numbers.'i' imaginary unit .<math>i=\sqrt{-1}</math>. | *where x&y are the real numbers.'i' imaginary unit .<math>i=\sqrt{-1}</math>. | ||
| − | *The square root of a complex number is defined by | + | *The square root of a complex number is defined by: |
| − | *where r is the modulus of z. <math>r=\sqrt{x^2+y^2}</math> | + | <math>\sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^iθ}=\sqrt{r}(cos(θ/2)+isin(θ/2)</math> |
| − | *And θ is the argument of z. <math> θ=tan^{-1}(y/x)</math> also θ∈(-Pi(),Pi()]. | + | *where <math>r</math> is the modulus of <math>z</math>. <math>r=\sqrt{x^2+y^2}</math> |
| + | *And <math>\theta</math>θ is the argument of <math>z</math>. <math> θ=tan^{-1}(y/x)</math> also θ∈(-Pi(),Pi()]. | ||
*We can use COMPLEX function to convert real and imaginary number in to a complex number. | *We can use COMPLEX function to convert real and imaginary number in to a complex number. | ||
| − | |||
==Examples== | ==Examples== | ||
Revision as of 23:11, 18 December 2013
IMSQRT(z)
- is the complex number is of the form
is the complex number is of the form 
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".
- where x&y are the real numbers.'i' imaginary unit ..
- 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^iθ}=\sqrt{r}(cos(θ/2)+isin(θ/2)}
- where is the modulus of .
- And θ 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 θ=tan^{-1}(y/x)} also θ∈(-Pi(),Pi()].
- We can use COMPLEX function to convert real and imaginary number in to a complex number.
is the modulus of 
θ is the argument of Examples
- =IMSQRT("2+3i")=1.67414922803554+0.895977476129838i
- =IMSQRT("-4-5i")=1.09615788950152-2.2806933416653i
- =IMSQRT("7")=2.64575131106459
- =IMSQRT("8i")=2+2i
See Also