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Excel IMARGUMENT Function

The IMARGUMENT function returns the angle expressed in radians, known as the argument θ (theta), of a given complex number in x + yi or x + yj text format.

imargument function 1


Syntax

=IMARGUMENT(inumber)


Arguments

  • inumber (required): A complex number for which to calculate the argument θ.

Return Value

The IMARGUMENT function returns a numeric value.


Function Notes

  • inumber can be supplied as any of the following:
    • A real number whose imaginary part is 0, e.g., 1 is a complex number 1+0i; Or a purely imaginary number whose real part is 0, e.g., i is a complex number 0 + 1i;
    • A cell reference that refers to a complex number;
    • A complex number enclosed in double quotation marks.
  • inumber can be returned by the COMPLEX function which converts real and imaginary coefficients into a complex number.
  • IMARGUMENT will return the #NUM! error if inumber is not recognized as a complex number that has lowercase i or j (iota).
  • IMARGUMENT will return the #VALUE! error if inumber is a logical value.
  • To have the result shown in degrees, multiply the result by 180/PI(), i.e., IMARGUMENT(inumber)*180/PI().

Example

To calculate the theta argument in radians of the complex numbers listed in the below table, please copy or enter the formula below in the top cell, press Enter to get the result, and then drag the fill handle (at the lower right corner of the result cell) down to apply the formula to below cells.

=IMARGUMENT(B3)

imargument function 2

Also, you can type the actual complex number in the formula as shown below. Make sure the complex number is enclosed with double quotes:

=IMARGUMENT("3+4i")


Related functions

Excel COMPLEX Function

The COMPLEX function converts real and imaginary coefficients to a complex number of the form x + yi or x + yj.

Excel PI Function

The PI function returns the number 3.14159265358979 of the mathematical constant called pi.


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