# How to Use IMLN function in Google Sheets in 2020?

IMLN functionThe IMLN function returns the logarithm of a complex number, base e (Euler’s number).

Parts of a IMLN formula

The IMLN formula is formatted as =IIMLN(number).

Part
Description
Notes

number
The input value of the logarithm function.

The number can be written as plain numbers, e.g. 1, to be interpreted as a real number.
The number can be written as quoted text in order to specify both the real and complex coefficients.

Sample formulas

IMLN(“3+4i”)

IMLN(A2)

IMLN(“4+2j”)

Notes

IMLN is equivalent to LN for all non-complex values that are greater than zero.
IMLN is equivalent to LOG given base of e, or EXP(1), for all non-complex values that are greater than zero.
The natural logarithm of a complex number is defined as follows:

ln(x+yi) = √(x2+y2) + i tan-1(y/x)

Examples

A
B

1
Formula
Result

2
=IMLN(“1+i”)
0.346573590279973+0.785398163397448i

3
=IMLN(“4+2j”)
1.497866136777+0.463647609000806i

4
=IMLN(“-4.6”)
1.52605630349505+3.14159265358979i

Related functions

LN: Returns the the logarithm of a number, base e (Euler’s number).

COMPLEX: The COMPLEX function creates a complex number, given real and imaginary coefficients.

IMAGINARY: Returns the imaginary coefficient of a complex number.

IMREAL: Returns the real coefficient of a complex number.

LOG10: Returns the the logarithm of a number, base 10.

LOG: Returns the the logarithm of a number given a base.

EXP: Returns Euler’s number, e (~2.718) raised to a power.