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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 (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:

IMPOWER(inumber, number)

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.