Manuals/calci/IMLOG2

IMLOG2(z)

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

Description

• This function gives the binary logarithm of a complex number.
• $IMLOG2(z)$, where 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 z} is the complex number in the form of 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+iy} . i.e. 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} & 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 y} are the real numbers.
• 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 I} imaginary unit .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 i=\sqrt{-1}} .
• Binary logarithm is the inverse function of 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 n ↦ 2n} .
• Log base 2 is called Binary logarithm.
• To find the Binary logarithm of a complex number we have to calculate from the natural logarithm.
• So 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 log2(x+iy)=(log_2 e)ln(x+iy)} .
• We can use COMPLEX function to convert real and imaginary number in to a complex number.

Examples

1. =IMLOG2("2+3i") = 1.85021985921295+1.41787163085485i
2. =IMLOG2("5-6i") = 2.96536866900967-1.26388460522614i
3. =IMLOG2("15") = 3.90689059590921
4. =IMLOG2("11i") = 3.45943161890355+2.26618007108801i
5. =IMLOG2("0") = NULL

See Also

• IMLOG10
• LOG2
• COMPLEX

References

Binary Logarithm