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 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.