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
-
IMLNis equivalent toLNfor all non-complex values that are greater than zero. -
IMLNis equivalent toLOGgiven base ofe, orEXP(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) = √(x 2 +y 2 ) + 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 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 logarithm of a number, base 10.
LOG
: Returns the logarithm of a number given a base.
EXP
: Returns Euler's number, e (~2.718) raised to a power.
