Manuals/calci/IMSQRT

IMSQRT(Complexnumber)


  • 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.  imaginary unit . .
  • The square root of a complex number is defined by:

Failed to parse (syntax error): {\displaystyle \sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^{i\theta}}=\sqrt{{r}(cos(\frac{θ}{2})+isin(\frac{θ}{2})}}

  • where   is the modulus of  .  
  • And   is the argument of  . Failed to parse (syntax error): {\displaystyle θ=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 θ∈(-\pi,\pi]} .
  • We can use COMPLEX function to convert real and imaginary number in to a complex number.

ZOS Section

  • 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")=2.64575131106459
  4. =IMSQRT("8i")=2+2i

See Also


References

Binary Logarithm