/sci/ - Science & Math » Thread #11919794

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Log(x) * -1 = a-bi format?

Anonymous Mon 20 Jul 18:51:10 2020 No.11919794 View Reply Original Report

Quoted By: >>11919800 >>11919867 >>11919886

Why is this? I don’t understand what is going on

Anonymous

Anonymous Mon 20 Jul 2020 18:52:29 No.11919800 Report

Quoted By:

>>11919794
You cannot take the log of a negative number.

Anonymous

Anonymous Mon 20 Jul 2020 19:10:46 No.11919867 Report

Quoted By:

>>11919794
>>11919794 (In R, you can't. That's not true in C though)
You can represent a negative number as an the product of an exponential to a complex power and the magnitude using the Taylor series for exp(z)(which is what the calculator is using to calculate log(-3)). However, to make it unique, usually the domain is from (-?,?]:
https://en.wikipedia.org/wiki/Complex_number#Complex_exponential_and_related_functions

Anonymous

Anonymous Mon 20 Jul 2020 19:16:57 No.11919886 Report

Quoted By:

>>11919794
log(-3) = ln(-3)/ln(10) = C * ln(-3) -> e^x = -3 = e^Re(x) * e^Im(x) -> Im(x) = pi -> e^Im(x) = -1, Re(x) = ln(3) -> e^Re(x) = 3.

x = 1.09 + i*pi = ln(-3)
x/ln(10) = 0.477 - 1.36

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