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.

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