The IMABS function is used to find the absolute value of a complex number. It takes a complicated formula and turns it into a ready-to-use function.
Contents:
Syntax
= IMABS(complex_number)complex_number - This is the complex number for which you want to find the absolute value. It can be supplied as a string (like "3+4i") or as a reference to a cell containing the complex number.
Explanation
The IMABS function is part of the "Engineering" group of functions within Excel.
This function takes a complex number, then calculates the square of both the real part, and the imaginary part, adds them up, and then finds the square root of this sum.
What is the Absolute Value of a Complex Number?
Firstly, to understand the IMABS function, you need to know what a complex number is and what we mean by its absolute value.
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit (i² = -1).
The absolute value (or modulus) of a complex number is the distance of that number from the origin (0,0) in the complex plane. Mathematically, for a complex number a + bi, its absolute value is √(a² + b²).
As an example, if you have the complex number: 3+4i, and wanted to take the absolute value of that number, it would look like √(3² + 4²), or in Excel terms:
= SQRT(3^2+4^2)Examples
How to Find the Absolute Value of a Complex Number
Let's say we have table with complex numbers, and need to find their absolute values.
Without the IMABS function, to find the absolute value of a complex number in cell A2, we would need to use this formula:
= SQRT(IMREAL(A2)^2+IMAGINARY(A2)^2)This formula strips out the real and imaginary parts of a complex number and calculates the absolute value.
But, if we use the IMABS function, this can all be done in one easy step, with one formula.
Simple reference a complex number in your formula, and the function will do the rest.
If you want to use a hardcoded number instead of a cell reference, be sure to wrap the complex number in quotation marks like so:
= IMABS("3+4i")