A to Z of Excel Functions: the IMPOWER Function
26 October 2020
Welcome back to our regular A to Z of Excel Functions blog. Today we look at the IMPOWER function.
The IMPOWER function
This function is kind of IMPOWERing…
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.
Sometimes you might wish to raise a complex number to a power. IMPOWER returns a complex number that is in the x + yi or x + yj text format to a given power.
The IMPOWER function employs the following syntax to operate:
The IMPOWER function has the following arguments:
- inumber: this is required and represents the complex number you wish to raise to a power
- number: this is also required. This is the power to which you wish to raise the complex number.
It should be further noted that:
- you should use COMPLEX to convert real and imaginary coefficients into a complex number
- IMPOWER recognises either the i or j notation
- if inumber is a value that is not in the x + yi or x + yj text format, IMPOWER returns the #NUM! error value
- if inumber is a logical value, IMPOWER returns the #VALUE! error value
- if number is non-numeric, IMPOWER returns the #VALUE! error value
- 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 IMPOWER will return an #NUM! error
- a complex raised to a power is calculated as follows:
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 here.