The IMARGUMENT function returns the argument  \theta (theta), an angle expressed in radians, such that: 

    \[  x+yi = |x+yi|^{i\theta} = |x+yi|(cos\theta + sin\theta) \]




Argument Description
inumber A complex number for which you want the argument \theta

Note: Use the COMPLEX function to convert real and imaginary coefficients into a complex number.


  A B C D
1 Data Formula Result Notes
2 3+4i =IMARGUMENT(A2) 0.92729522 Theta argument of 3+4i, in radians
3   =IMARGUMENT(“3+4i”) 0.92729522  
4   =IMARGUMENT(“3i”) 1.570796327  
5   =IMARGUMENT(COMPLEX(4,1)) 0.244978663  

Common Function Error(s)

Problem What went wrong
#NUM! Occurs if the supplied inumber argument is not recognized as a complex number
#NAME? Occurs when Analysis ToolPak add-in is not enabled

IMARGUMENT is calculated as:

    \[ \text{IMARGUMENT}(z) = \tan^{-1} \left( \frac{y}{x} \right) = \theta  \]


  • \theta\epsilon(-\pi; \pi), and
  • z = x + yi