The IMARGUMENT function returns the angle (also known as the argument, or theta) of the given complex number in radians. This is the angle θ such that, for any complex number in Cartesian form x + yi, x + yi = reiθ where r is the magnitude of the number.
Parts of an IMARGUMENT formula
=IMARGUMENT(number)
| Part | Description | Notes |
| number | The complex number whose argument will be calculated. |
This can be either the result of the COMPLEX function, a real number (which is interpreted as a complex number with imaginary part equal to 0), or a string in the format “x + yi” where x and y are numeric. |
Sample formulas
IMARGUMENT(COMPLEX(4, 6)
IMARGUMENT(4)
IMARGUMENT("2+3I")
Notes
The IMARGUMENT function returns an error if the given number isn't a valid complex number, or is 0.
Examples
| A | B | |
| 1 | Formula | Result |
| 2 | =IMARGUMENT(COMPLEX(0, 1)) | 1.570796327 |
| 3 | =IMARGUMENT(1) | 0 |
| 4 | =IMARGUMENT("1+1i") | 0.7853981634 |
Related function
COMPLEX: The COMPLEX function creates a complex number, given real and imaginary coefficients.