# Documentation/Calc Functions/IMSUM

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## Function name:

IMSUM

## Category:

Add-in

## Summary:

Calculates the sum of multiple complex numbers.

## Syntax:

IMSUM(**Complex 1** [; **Complex 2** [; … [; **Complex 255**]]])

## Returns:

Returns a text string giving the complex number that results from adding together the complex numbers passed as arguments.

## Arguments:

**Complex 1** is a string (in quotation marks) representing a complex number in the form *a+bi* or *a+bj*, or a reference to one or more cells containing such strings, which are the complex numbers to be added together. *a* and *b* are real numbers.

**Complex 2** ... **Complex 255** are as **Complex 1**.

- If any of the complex numbers passed to IMSUM does not have an imaginary part (
*b*equal to 0), the real part can be passed to IMSUM as a number rather than a string. - If any of the strings passed to IMSUM is not a valid complex number, or any of the referenced cells contain an invalid complex number, IMSUM reports an invalid argument error (Err:502).
- It is possible for the arguments passed to IMSUM to contain no complex numbers. In this case IMSUM returns 0.
- If the complex numbers passed to IMSUM use different imaginary units (
*i*or*j*), IMSUM returns the result using the imaginary unit of the first complex number processed.

## Additional details:

### Details specific to IMSUM function

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

The equation is applied repeatedly depending how many complex numbers are specified in the arguments.

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

=IMSUM("3+4j"; "5-3i") | Here the function adds two complex numbers and returns the result using the imaginary unit of the first complex number. | 8+j |

=IMSUM("3.4+5.6i"; 7.8) | Here the function adds the complex number in the first argument to the real number in the second argument (which is passed as a number rather than a string). | 11.2+5.6i |

=IMSUM(E1; E2; E3) where cells E1, E2, and E3 contain the complex numbers 1+2i, 3-4i, and -5+6i respectively. | Here the function adds the three complex numbers in cells E1, E2, and E3 (identified as separate arguments). | -1+4i |

=IMSUM(E1:E3) where cells E1, E2, and E3 contain the complex numbers 1+2i, 3-4i, and -5+6i respectively. | Here the function again adds the three complex numbers in cells E1, E2, and E3 (identified as a cell range in a single argument). | -1+4i |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

IMSUM