# Manuals/calci/IMLN

IMLN(Complexnumber)

• is of the form .
• IMLN(),returns the natural logarithm of a complex number.

## Description

• This function gives the Natural Logarithm of a complex number.
• In , where Complexnumber is in the form of . i.e & are the real numbers.
• And is the imaginary unit .
• Normally Complex logarithm function is an inverse of the Complex exponential function.
• A logarithm of is a complex number such that and it is denoted by .
• If with & are real numbers then natural logarithm of a complex number :

adding integer multiples of gives all the others.

• We can use COMPLEX function to convert real and imaginary number in to a complex number.

## ZOS

• The syntax is to calculate the natural logarithm of a complex number in ZOS is .
• is of the form
• For e.g.,IMLN("10+17i")
Natural Logarithm of a Complex Number

## Examples

1. IMLN("3-2i")=1.28247467873077-0.588002603547568i
2. IMLN("6+7i")=2.22132562824516+0.862170054667226i
3. IMLN("4")=1.38629436111989 +0i
4. IMLN("10i")=2.30258509299405+1.5707963267949i

## Related Videos

Log of Complex Number