How to Use the IMARGUMENT Function in Excel

Today, we’ll delve into the IMARGUMENT function, a valuable tool available in both Microsoft Excel and Google Sheets. This function is used for deriving the argument (or angular component) of a complex number.

Function Syntax

The syntax for the IMARGUMENT function is consistent across Excel and Google Sheets:

IMARGUMENT(inumber)

Where:

  • inumber (required): The complex number whose argument you wish to determine.

Usage and Examples

Example 1: Finding the Argument of a Complex Number

Consider a complex number 3+4i. To find its argument, you would use the IMARGUMENT function as follows:

Formula Result
=IMARGUMENT(3+4i) 0.93 radians (approximately 53.13 degrees)

In this case, the IMARGUMENT function computes the argument of the complex number 3+4i to be roughly 0.93 radians, or 53.13 degrees.

Example 2: Using IMARGUMENT in a Real-World Scenario

Imagine working on an electrical circuit project involving complex impedances. You have the magnitude of an impedance and its angle, and you need to express this as a complex number for further analysis.

Assume the impedance has a magnitude of 5 units and an angle of 30 degrees. To find the complex number representation, use IMARGUMENT in combination with other functions such as IMABS and IMSIN. The progression is as follows:

Formula Result
=IMARGUMENT(5*IMEXP(IMAGINARY(30*PI()/180))) 0.52 radians (approximately 29.74 degrees)

This example first converts the angle from degrees to radians (30 degrees to 0.52 radians), then applies the IMARGUMENT function along with IMEXP and IMAGINARY to obtain the complex number representation.

The IMARGUMENT function proves to be incredibly useful in a variety of contexts, including engineering, science, and mathematics, particularly where complex numbers play a crucial role.

More information: https://support.microsoft.com/en-us/office/imargument-function-eed37ec1-23b3-4f59-b9f3-d340358a034a

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Returns the modified Bessel function In(x)
Returns the Bessel function Jn(x)
Returns the modified Bessel function Kn(x)
Returns the Bessel function Yn(x)
Converts a binary number to decimal
Converts a binary number to hexadecimal
Converts a binary number to octal
Returns a 'Bitwise And' of two numbers
Returns a value number shifted left by shift_amount bits
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Returns a value number shifted right by shift_amount bits
Returns a bitwise 'Exclusive Or' of two numbers
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Converts a number from one measurement system to another
Converts a decimal number to binary
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Returns the error function
Returns the error function
Returns the complementary error function
Returns the complementary ERF function integrated between x and infinity
Tests whether a number is greater than a threshold value
Converts a hexadecimal number to binary
Converts a hexadecimal number to decimal
Converts a hexadecimal number to octal
Returns the absolute value (modulus) of a complex number
Returns the imaginary coefficient of a complex number
Returns the complex conjugate of a complex number
Returns the cosine of a complex number
Returns the hyperbolic cosine of a complex number
Returns the cotangent of a complex number
Returns the cosecant of a complex number
Returns the hyperbolic cosecant of a complex number
Returns the quotient of two complex numbers
Returns the exponential of a complex number
Returns the natural logarithm of a complex number
Returns the base-10 logarithm of a complex number
Returns the base-2 logarithm of a complex number
Returns a complex number raised to an integer power
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Returns the hyperbolic secant of a complex number
Returns the sine of a complex number
Returns the hyperbolic sine of a complex number
Returns the square root of a complex number
Returns the difference between two complex numbers
Returns the sum of complex numbers
Returns the tangent of a complex number
Converts an octal number to binary
Converts an octal number to decimal
Converts an octal number to hexadecimal