# Documentation/Calc Functions/COMPLEX

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## Function name:

COMPLEX

## Category:

Add-in

## Summary:

Constructs a complex number as text, given its real and imaginary parts.

## Syntax:

COMPLEX(**RealNumber**; **ImaginaryNumber**[; **Suffix**])

## Returns:

Returns a text string which is the complex number constructed from the given real and imaginary parts, using the given or default imaginary unit.

## Arguments:

**RealNumber** is a real value, or a reference to a cell containing that value, which is the real part of the complex number.

**ImaginaryNumber** is a real value, or a reference to a cell containing that value, which is the imaginary part of the complex number.

**Suffix** is the string, or a reference to a cell containing that string, which comprises the letter to be used as the imaginary unit; either “i” or “j” (lowercase only). If omitted, “i” is used.

- If either
**RealNumber**or**ImaginaryNumber**is non-numeric, then COMPLEX reports a #VALUE! error. - If
**Suffix**is set to something other than “i” or “j”, COMPLEX reports an invalid argument error (Err:502).

## Additional details:

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

=COMPLEX(1; 2) | Here the function returns the complex number string using the default "i" as the imaginary unit. | 1+2i |

=COMPLEX(-3; 4; "j") | Here the function returns the complex number string using the specified "j" as the imaginary unit. | -3+4j |

=COMPLEX(F1; F2; F3) where cells F1 and F2 contain the values 1.23 and -4.56 respectively and cell F3 contains the character "j". | Here the function returns the complex number string constructed using values entered in the specified cells. | 1.23-4.56j |

=COMPLEX(1.2E17; 3.4E16) | Here the function returns the complex number string using real and imaginary parts specified in scientific (E) notation. | 1.2e+17+3.4e+16i |

## Related LibreOffice functions:

None.

## ODF standard:

## Equivalent Excel functions:

COMPLEX