Difference between revisions of "Manuals/calci/IMSQRT"

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*For e.g.,IMSQRT("9+10i")
*For e.g.,IMSQRT("9+10i")
{{#ev:youtube|ofW56najtOE|280|center|Imaginary Square Root}}

Revision as of 01:21, 3 July 2014


  • is of the form


  • 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 (syntax error): {\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


  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


Binary Logarithm