Manuals/calci/IMLN

IMLN(z)

• $z$ is the complex number is of the form $x+iy$

Description

• This function gives the natural logarithm of a complex number.
• In IMLN(z),Where z is the complex number in the form of "x+iy".i.e. x&y are the real numbers.
• 'I' imaginary unit .i=sqrt(-1).
• A logarithm of z is a complex number w such that z = e^w and it is denoted by ln(z).
• If z = x+iy with x&y are real numbers then natural logarithm of a complex number : $ln(z)=w=ln(|z|)+iarg(z)=ln(sqrt(x^{2}+y^{2})+itan^{-}1(y/x$ adding integer multiples of 2πi gives all the others.
• We can use COMPLEX function to convert real and imaginary number in to 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 But calci is not considering the zero value of imaginary value of z.
4. IMLN("10i")=2.30258509299405+1.5707963267949i

See Also

• IMLOG10
• IMLOG2
• COMPLEX

References

Bessel Function