# Documentation/Calc Functions/IMSQRT

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## Function name:

IMSQRT

## Category:

Add-in

## Summary:

Calculates the principal square root of a complex number.

## Syntax:

IMSQRT(**ComplexNumber**)

## Returns:

Returns a text string giving the complex number that is the principal square root of the complex number passed as argument. The real part of the principal square root is non-negative, and its imaginary part has the same sign as the original complex number.

## Arguments:

**ComplexNumber** is a string (in quotation marks) representing a complex number in the form *a+bi* or *a+bj*, or a reference to a cell containing that string, whose square root is to be determined. *a* and *b* are real numbers.

- If
**ComplexNumber**does not have an imaginary part (*b*equal to 0), the real part can be passed to IMSQRT as a number rather than a string. - If
**ComplexNumber**is not a valid complex number, IMSQRT reports an invalid argument error (Err:502).

## Additional details:

### Details specific to IMSQRT function

For a complex number of the form *a+bi*, IMSQRT implements the following equation:

*sign(b) * ensures that the imaginary part of the complex number passed in the argument has the same sign as its principal square root.

### General information about Calc's handling of complex numbers

- A complex number is
**a number that can be expressed in the form**, where*a*+*bi**a*and*b*are real numbers and*i*is a symbol for the imaginary unit, such that*i*^{2}=−1.*a*is known as the real part of the complex number and*b*is known as its imaginary part.

- In some disciplines using
*i*to indicate the imaginary unit may be undesirable and, in such cases,**the symbol**. The functions provided by Calc to process complex numbers can use either*j*may be used instead*i*or*j*.

- For additional
**general background information**, visit Wikipedia’s Complex number page.

- Within Calc,
**a complex number is represented as a string expression**of the form "a+bi" or "a+bj", where*a*and*b*are real numbers. If the complex number happens to be a real number (*b*=0), then it can be represented as either a string expression or a numeric value. Complex number string expressions should not contain any space characters. Examples of valid Calc complex numbers include "2", -6, "2+3i", "3j", "12.34+56.78i", and "1e+23-1e-22j". Calc would not recognize the strings "1+j2", "i+1", and "i+j" as valid complex numbers.

- The representation of the complex numbers in strings can have
**up to 15 significant digits**and scientific style is automatically used if needed (visit Wikipedia’s Scientific notation page for more information). The decimal delimiter in complex number string expressions is always a dot, irrespective of locale setting.

## Examples:

Formula | Description | Returns |
---|---|---|

=IMSQRT("1.2-3.4j") | Here the function calculates the principal square root of a complex number that has non-zero real and imaginary parts. | 1.55008891284726-1.0967112827595j |

=IMSQRT("-i") | Here the function calculates the principal square root of a complex number that has no real part. The result has non-zero real and imaginary parts. | 0.707106781186547-0.707106781186547i |

=IMSQRT(-1) | Here the function calculates the principal square root of a negative real number. The result has no real part. | i |

=IMSQRT(F1) where cell F1 contains the complex number 2-3j. | Here the function calculates the principal square root of a complex number that is entered in a cell. | 1.67414922803554-0.895977476129838j |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

IMSQRT