IMARGUMENT functionThe 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.