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# A to Z of Excel Functions: The IMLN Function

5 October 2020

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

The IMLN function 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 wish to calculate the natural logarithm of a complex number.  The natural logarithm of a complex number is given by The IMLN function employs the following syntax to operate:

IMLN(inumber)

The IMLN function has the following argument:

• inumber: this is required and represents the complex number for which you wish to calculate the natural logarithm.

It should be further noted that:

• you should use >COMPLEX to convert real and imaginary coefficients into a complex number
• IMLN recognises either the i or j notation
• if inumber is a value that is not in the x + yi or x + yj text format, IMLN returns the <>#NUM! error value
• if inumber is a logical value, IMLN 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 IMLN 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 here.