# A to Z of Excel Functions: the IMPRODUCT Function

9 November 2020

*Welcome back to our regular A to Z of Excel Functions blog. Today we look at the IMPRODUCT function. *

**The IMPRODUCT 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 **i ^{2}** = −1. In general, the square of an imaginary number

**bi**is

**−b**. For example, 9

^{2}**i**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 **rea**l 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 multiply complex numbers together. **IMPRODUCT **returns the product of one to 255 complex numbers in the **x + yi** or **x + yj** text format.

The **IMPRODUCT **function employs the following syntax to operate:

**IMPRODUCT(inumber1, [inumber2], …)**

The **IMPRODUCT** function has the following arguments:

**inumber1, inumber2, …:**the first argument is required (the remainder are optional). This / these represent(s) the complex number(s) you wish to multiply.

It should be further noted that:

- you should use
**COMPLEX**to convert real and imaginary coefficients into a complex number **IMPRODUCT**recognises either the**i**or**j**notation- if any of
**inumber1, [inumber2], …**is a value that is not in the**x + yi**or**x + yj**text format,**IMPRODUCT**returns the*#NUM!*error value - if any of
**inumber1, [inumber2], …**is a logical value,**IMPRODUCT**returns the*#VALUE!*error value - if any of
**inumber1, [inumber2], …**is non-numeric,**IMPRODUCT**returns the*#VALUE!*error value - if any 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**IMPRODUCT**will return an*#NUM!*error - the product of two complex numbers is:

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. *