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 $z<math>isthecomplexnumberintheformof<math>x+iy$. i.e Failed to parse (syntax error): {\displaystyle x<math> & <math>y<math> are the real numbers. *<math>I} imaginary unit $i=sqrt{-1}<math>.*Alogarithmof<math>z$ is a complex number w such that $z=e^{w}$ and it is denoted by $ln(z)$.
• If $z=x+iy$ with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x<math> & <math>y} are real numbers then natural logarithm of a complex number :

$ln(z)=w=ln(|z|)+iarg(z)=ln({\sqrt {x^{2}+y^{2}}}+itan^{-1}({\frac {y}{x}}$ adding integer multiples of $2\pi i$ 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