A to Z of Excel Functions: the IMABS Function
15 June 2020
Welcome back to our regular A to Z of Excel Functions blog. Today we look at the IMABS function.
The IMABS function
An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i (sometimes denoted j) which is defined by its property i2 = −1. In general, the square of an imaginary number bi is −b2. For example, 9i is an imaginary number, and its square is −81. Zero is considered to be both real and imaginary.
An imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where the real numbers a and b are called, respectively, the real part and the imaginary part of the complex number.
Just like the Excel function ABS measures the “distance” between a number and zero (0) (e.g. ABS(-5) is five (5) units from zero (0), therefore, ABS(-5) = 5), so IMABS(“a + bi”) measures the distance from zero (0) to the point z = a + bi. As can be clearly seen in the diagram, this distance is given by Pythagoras’ Theorem
Technically, IMABS returns the absolute value, or modulus, of a complex number a + bi, provided the number has been provided in said text format.
The IMABS function employs the following syntax to operate:
The IMABS function has the following argument:
- inumber: this is required and represents the complex number for which you want the absolute value.
It should be further noted that:
- you should use COMPLEX to convert real and imaginary coefficients into a complex number
- IMABS recognises either the i or j notation
- if the complex number ends in +i or -i (or j), i.e. there is no coefficient between the operator and the imaginary unit, there must be no space, otherwise IMABS will return an #NUM! error.
Please see my example below:
We’ll continue our A to Z of Excel Functions soon. Keep checking back – there’s a new blog post every business day.
A full page of the function articles can be found.