The Excel IMARGUMENT function returns the argument θ, (an angle expressed in radians), of a supplied complex number.
θ is the angle that satisfies the following equation:
Syntax: IMARGUMENT( inumber )
The IMARGUMENT function syntax has the following arguments:
 Inumber Required. A complex number for which you want the argument θ
Example: Let’s look at some Excel IMARGUMENT function examples and explore how to use the IMARGUMENT function as a worksheet function in Microsoft Excel:
Syntax: =IMARGUMENT(A2)
Result:
Based on the Excel spreadsheet above, the following IMARGUMENT examples would return:
Syntax: =IMARGUMENT(A3)
Result: 0.463647609
Syntax: =IMARGUMENT(A4)
Result: 0
Syntax: =IMARGUMENT(A5)
Result: 1.570796327
Syntax: =IMARGUMENT(A6)
Result: 0.463647609
Syntax: =IMARGUMENT(A7)
Result: 1.570796327
Syntax: =IMARGUMENT(A8)
Result: 1.165904541
Syntax: =IMARGUMENT(A9)
Result: 0.927295218
Syntax: =IMARGUMENT(A10)
Result: 0.643501109
Syntax: =IMARGUMENT(A11)
Result: 1.176005207
Syntax: =IMARGUMENT(A12)
Result: 0.291456794
Syntax: =IMARGUMENT(A13)
Result: 0.927295218
Note:
 Use COMPLEX to convert real and imaginary coefficients into a complex number.

IMARGUMENT is calculated as follows: where: and z = x + yi