# How to Use IMARGUMENT function in Google Sheets in 2020?

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.

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