Author: Oscar Cronquist Article last updated on September 23, 2022

How to use the IMARGUMENT functionv2

The IMARGUMENT function calculates the argument theta θ which is an angle displayed in radians.

1. IMARGUMENT Function Syntax

IMARGUMENT(inumber)

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2. IMARGUMENT Function Arguments

inumber Required. A complex number in x+yi or x+yj text format.

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3. IMARGUMENT function example

How to use the IMARGUMENT function

The image above shows how to calculate the θ based on complex numbers specified in column C.

Formula in cell D3:

=IMARGUMENT(C3)

A complex number can be described as z = x + yi or z = x + yj text form in Excel.

The IMARGUMENT function calculates theta θ expressed in radians using this formula:

θ = tan-1(y/x) for x>0

3.1 Explaining formula

Step 1 - Populate arguments

IMARGUMENT(inumber)

becomes

IMARGUMENT(C3)

Step 2 - Evaluate IMARGUMENT function

IMARGUMENT(C3)

becomes

IMARGUMENT("9+12i")

and returns

0.927295218001612

Here is how 0.927295218001612 is calculated:

tan θ = y/x

becomes

θ = tan-1(y/x)

tan-1(y/x)

becomes

tan-1(12/9)

equals

0.927295218001612

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