In this article, we will learn about how to use the IMLOG10 function in Excel.

COMPLEX number (inumber) in excel derived for mathematical number having real and imaginary coefficients. In mathematics we call it the coefficient of **i **or **j **(iota).

i = √-1

Square root of negative number is not possible, so for calculation purpose, ?-1 is named as imaginary and call it **iota (i **or **j)**. For calculation of some term like shown below.

= 2 +√-25

= 2 +√-1*25

= 2 +√-1*25

= 2 +√-1* 5

= 2 + 5i

This here equation is a Complex number (inumber) having 2 different parts called **real part **& **imaginary part**

The coefficient of **iota **(**i**) which is **5** is called as imaginary part and the other part **2 **is called the real part of the complex number.

Complex number (inumber) is written in the X + iY format.

common logarithm of a complex number (X + iY) is given by:

log_{10} ( X +iY) = log_{10}(e) log_{e} ( X +iY) = log_{10}(e) [ log_{e}√X^{2} +Y^{2} + i tan^{-1}(Y/X) ]

Here X & Y are the coefficients of the real & imaginary part of the complex number (inumber).

Here:

- log at the base
**10**is called the common logarithm of a number. - log at the base
**e**is called the natural logarithm of a number where e = 2.7182…(approx). - Coefficient of iota is inverse tan function of ( Y / X )tan
^{-1}(Y/X)which returns the angle in radians.

log10( X +iY) =log_{10}(e) [ ln √X^{2} +Y^{2} + i tan^{-1}(Y/X)]

The IMLOG10 function returns the complex common logarithm of the complex number (inumber) having both real & imaginary part.

**Syntax:**

=IMLOG10 (inumber)

inumber : complex number on which common logarithm is performed.

Let’s understand this function using it in an example.

Here we have values where we need to get the complex common logarithm of the input complex number (inumber)

Use the formula:

=IMLOG10 (A2)

A2 : complex number (inumber) provided as cell reference.

As you can see the complex number having real_num = 4 & imaginary part = 3. The formula returns the complex common logarithm of the complex number.

common logarithm of a complex number (4 + 3i) = log_{10} (4 + 3i) = log_{10}(e)[ ln (4 +3i)] = log_{10}(e)[ ln √4^{2} +3^{2} + i tan^{-1}( 3 / 4 )]

Now copy the formula to the other remaining cells using **Ctrl + D** shortcut key.

As you can see the IMLOG10 function formula giving results just fine.

The table here explains more about the input real & imaginary part.

inumber | Real part (X) | Imaginary part (Y) |

i = 0 + 1i |
0 | 1 |

1 = 1 + 0i |
1 | 0 |

**Note:**

The formula returns the #NUM! error if the complex number doesn’t have lower case **i** or **j **(iota) otherwise the excel treats it as text rather than a complex number.

Hope you understood how to use IMLOG10 function and referring cell in Excel. Explore more articles on Excel mathematical functions here. Please feel free to state your query or feedback for the above article.

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