Manuals/calci/IMSQRT

IMSQRT(z)

• $z$ is the complex number is of the form $x+iy$

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 .$i={\sqrt {-1}}$.
• 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 $r$ is the modulus of $z$. $r={\sqrt {x^{2}+y^{2}}}$
• And $\theta$ is the argument of $z$. 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.

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

• IMREAL
• IMSUM
• IMAGINARY
• COMPLEX

References

Binary Logarithm