# IMARGUMENT function

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 = re 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.