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 toLN
for all non-complex values that are greater than zero.IMLN
is equivalent toLOG
given 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) = √(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 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.