# Documentation/Calc Functions/IMARGUMENT

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## Function name:

IMARGUMENT

## Category:

Add-in

## Summary:

Calculates the principal value of the argument of a complex number.

## Syntax:

IMARGUMENT(**ComplexNumber**)

## Returns:

Returns a real number in the range -π < φ ≤ π which is the argument (in radians) of the specified 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 argument is to be calculated. *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 IMARGUMENT as a number rather than a string. - If both real and imaginary parts of
**ComplexNumber**are 0, IMARGUMENT reports an invalid argument error (Err:502). - If
**ComplexNumber**is not a valid complex number, IMARGUMENT reports an invalid argument error (Err:502).

## Additional details:

### Details specific to IMARGUMENT function

A complex number of the form *a+bi* can be written in trigonometric form as a+bi = r(cos*φ*+isin*φ*), where r is the absolute value or modulus of the complex number and *φ* is its argument.

IMARGUMENT calculates the argument of the complex number using the formula:

and then if b < 0, *φ* = -*φ*.

For more information about arguments of complex numbers, visit Wikipedia's Argument (complex analysis) page.

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

=IMARGUMENT("3.4+4.5j") | Here the function calculates the argument of a complex number that has non-zero real and imaginary parts. | 0.923749 |

=IMARGUMENT("-i") | Here the function calculates the argument of a complex number that has no real part. | -1.570796 |

=IMARGUMENT(-1) | Here the function calculates the argument of a complex number that has no imaginary part. | 3.141593 |

=IMARGUMENT(F1) where cell F1 contains the complex number 2-3j. | Here the function calculates the argument of a complex number that is entered in a cell. | -0.982794 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

IMARGUMENT