# Documentation/Calc Functions/IMDIV

TDF LibreOffice Document Liberation Project Community Blogs Weblate Nextcloud Redmine Ask LibreOffice Donate

## Function name:

IMDIV

## Category:

Add-in

## Summary:

Calculates the result of dividing one complex number by another.

## Syntax:

IMDIV(**Numerator**; **Denominator**)

## Returns:

Returns a text string giving the complex number that results from dividing one complex number by another.

## Arguments:

**Numerator** 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, which is the numerator or dividend of the division operation.

**Denominator** is a string (in quotation marks) representing a complex number in the form *c+di* or *c+dj*, or a reference to a cell containing that string, which is the denominator or divisor of the division operation.

- If either
**Numerator**or**Denominator**does not have an imaginary part (*b*or*d*equal to 0), that argument’s real part can be passed to IMDIV as a number rather than a string. - If both real and imaginary parts of
**Denominator**are 0, IMDIV reports an invalid argument error (Err:502). - If either
**Numerator**or**Denominator**is not a valid complex number, IMDIV reports an invalid argument error (Err:502). - If
**Numerator**and**Denominator**use different imaginary units (*i*or*j*), IMDIV returns the result using the imaginary unit of**Numerator**.

## Additional details:

### Details specific to IMDIV function

For complex numbers of the form *a+bi* and *c+di*, IMDIV implements the following equation:

### 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 |
---|---|---|

=IMDIV("-238+240i";"10+24i") | Here the function calculates the result of dividing the first complex number by the second. | 5+12i |

=IMDIV("9+8j"; "1+2i") | Here the function calculates the result of dividing the first complex number by the second, using the imaginary unit of the first argument. | 5-2j |

=IMDIV(3; -2) | Here the function calculates the result of dividing the first real number by the second. | -1.5 |

=IMDIV(E1; E2) where cells E1 and E2 contain the complex numbers 1.2-3.4i and 5.6+7.8j respectively. | Here the function calculates the result of dividing the first complex number by the second, with both entered in cells. | -0.214750542299349-0.308026030368764i |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

IMDIV