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Engineering - IMSQRT Function
Description
The IMSQRT function returns the square root of a complex number in x + yi or x + yj text format. The square root of a complex number is −
$$\sqrt{x+yi}=\sqrt{r}\cos\left ( \frac{\theta}{2} \right )+i\sqrt{r} \sin\left ( \frac{\theta}{2} \right )$$
Where −
$$r=\sqrt{x^2+y^2} \: \: \: and \: \: \: \theta = tan^{-1}\left ( \frac{y}{x} \right ) \: \: \: and \: \: \: \theta \epsilon (-\pi; \pi]$$
Syntax
IMSQRT (inumber)
Arguments
| Argument | Description | Required/ Optional |
|---|---|---|
| Inumber | A complex number for which you want the square root. | Required |
Notes
Complex Numbers in Excel are simply stored as text.
When a text string in the format "a + bi" or "a + bj" is supplied to one of Excel's built-in Complex Number Functions, this is interpreted as a complex number.
The complex number functions can accept a simple numeric value, as this is equivalent to a complex number whose imaginary coefficient is equal to 0.
Use COMPLEX to convert real and imaginary coefficients into a complex number.
If inumber is not recognized as a complex number, IMSQRT returns the #NUM! error.
If inumber is a logical value, IMSQRT returns the #VALUE! error.
Applicability
Excel 2007, Excel 2010, Excel 2013, Excel 2016
Example
