IMSQRT

Updated 2024-03-13 20:00:01.657000

Syntax

SELECT [westclintech].[wct].[IMSQRT] (
   <@inumber, nvarchar(4000),>)

Description

Use the scalar function IMSQRT to return the square root of a complex number in x + yi or x + yj text format. The square root of a complex number is computed by:

\sqrt{x+yi}=\sqrt{r}\left(\cos\frac{\theta}{2}+i\sin\frac{\theta}{2}\right)

Wherer = IMABS(@inumber)θ = IMARGUMENT(@inumber)

Arguments

@inumber

is the value at which to evaluate the function. @inumber is an expression of type varchar or of a type that can be implicitly converted to varchar and must be in the format x + yi or x + yj, where x is a real number that can be converted to float and yi (or yj) is an imaginary number, where the y part can be converted to float.

Return Type

nvarchar(4000)

Remarks

Use COMPLEX to convert real and imaginary coefficients into a complex number.

Examples

select wct.IMSQRT('7+24i');

This produces the following result.

{"columns":[{"field":"column 1"}],"rows":[{"column 1":"4+3i"}]}