# IMLN function

The `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.