Sep 11, 2020 · How to evaluate $$\\log(i)?$$ Also, how to evaluate $$\\log(3+4i)?$$ I am reading complex analysis and I know that logarithm is a multibranched function and is periodic. What I have …

Nov 29, 2013 · Does anyone know a closed form expression for the Taylor series of the function $f(x) = \\log(x)$ where $\\log(x)$ denotes the natural logarithm function?

3 Why are there two different types of graph for logarithmic functions loga X log a X for different range of base,i.e; for : 0 <a <1 0 <a <1 and a> 1 a> 1 ?

Apr 23, 2017 · The first link is simply using the basic rules for logarithms - the log of a product is equal to the sum of the logs (working in base 10).

Oct 11, 2015 · Here's a common definition: log z = log|z| + i arg z + i2πk log z = log | z | + i arg z + i 2 π k Where arg z arg z returns the argument or angle of the complex number z z. Note that the final …

May 2, 2015 · Easy way to remember Taylor Series for log (1+x)? Ask Question Asked 10 years, 8 months ago Modified 6 years, 6 months ago

5 If we defined log1 1 log 1 1, we would want it to satisfy the basic properties that log satisfies. One of these properties is aloga b = b a log a b = b Well, this is bad, because setting a = 1 a = 1, we find …

Whenever I see one write $\log (z_1z_2)=\log (z_1)+\log (z_2)$ without specifying the branches that are assumed, I begin to wonder if the analysis is sound. Of course, here one only needs to ensure that …

log1(1) log 1 (1) could be any number, because any number solves the equation 1x = 1 1 x = 1. This is a bad thing for a function (which is what we want the logarithm to be), so we leave it undefined.

Jan 10, 2021 · My teacher told me that the natural logarithm of a negative number does not exist, but $$\ln (-1)=\ln (e^ {i\pi})=i\pi$$ So, is it logical to have the natural logarithm of a negative number?