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#Engineering

IMARGUMENT

Excel Functions

Get the angle of a complex number

Syntax

EXCEL 
=IMARGUMENT(inumber)

Arguments

Parameter Description
inumber The complex number in the form "x+yi".

Return Value

The angle measured in radians

Details

The Excel IMARGUMENT function returns the angle of a complex number measured in radians. For example, given the complex number "3+4i" the function returns the angle 0.927295218. Geometrically, this value represents the angle between the positive real axis and the line on which the complex number lies in the complex plane. To convert the angle to degrees, use the DEGREES function. Given a complex number, many equivalent angles correspond to the line on which the number lies. For example, consider the complex number "-5-5i" in the complex plane. Starting from the positive real axis, you can rotate 225 degrees in the positive direction, or you can also rotate negative 135 degrees to get to "-5-5i". The IMARGUMENT function always returns angles in the range from -π to π radians. For the comple

Examples

Example 1

The Excel IMARGUMENT function returns the angle of a complex number measured in radians. For example, given the complex number "3+4i" the function ret

EXCEL 
=IMARGUMENT("3+4i") // returns 0.927295218
Example 2

To convert the angle to degrees, use the DEGREES function.

EXCEL 
=DEGREES(IMARGUMENT(COMPLEX(3,4))) // returns 53.13°
Explanation

The IMARGUMENT function always returns angles in the range from -π to π radians. For the complex number "-5-5i" the function returns the angle -3/4 π.

EXCEL 
=IMARGUMENT(COMPLEX(-5, -5)) // returns -3/4π
Explanation

For complex numbers that lie on the negative real axis, the function returns π radians.

EXCEL 
=IMARGUMENT(COMPLEX(-5, 0)) // returns π
Explanation

In other words, the range excludes -π and includes π. Given a complex number just below the negative real axis, the function returns an angle really c

EXCEL 
=IMARGUMENT(COMPLEX(-5, -0.01)) // returns -3.131592987

See Also

ATAN2 IMLN COMPLEX IMAGINARY