Manuals/calci/IMSQRT

IMSQRT (ComplexNumber)

• $ComplexNumber$ is of the form $z=x+iy$.
  • 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.$i$ imaginary unit .$i={\sqrt {-1}}$.
• Consider the complex number z.
• The square root of a complex number is defined by:

${\sqrt {z}}={\sqrt {x+iy}}={\sqrt {r.e^{i\theta }}}={\sqrt {{r}(cos({\frac {\theta }{2}})+isin({\frac {\theta }{2}})}}$

• where $r$ 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

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

• IMREAL
• IMSUM
• IMAGINARY
• COMPLEX

References

Binary Logarithm

• List of Main Z Functions

• Z3 home