What are complex numbers, actually? You can prove $1=-1$ and a complex cosine function can have value greater than $1$ and so on, there are many unexpected results when we use complex numbers. So, what are they actually? Do, they have any physical meaning or are they just a method in mathematics to manipulate numbers?
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- 2$\begingroup$ How can you prove $1=-1$? $\endgroup$Anthony Carapetis– Anthony Carapetis2013-09-22 09:56:21 +00:00Commented Sep 22, 2013 at 9:56
- $\begingroup$ Here the link-brilliant.org/assessment/techniques-trainer/… .Actually the proof has a small mistake(you can easily identify it) but however complex numbers give weird results in some cases. $\endgroup$Rajath Radhakrishnan– Rajath Radhakrishnan2013-09-22 09:59:41 +00:00Commented Sep 22, 2013 at 9:59
- 4$\begingroup$ The point of that question is that it is wrong. Even using complex numbers, there is no way to prove $1=-1$, nor are there other contradictory results. $\endgroup$robjohn– robjohn ♦2013-09-22 10:05:14 +00:00Commented Sep 22, 2013 at 10:05
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1 A complex number is a number that has both Real and Imaginary Components, It is the the form $$a+bi$$ where $i$ is defined as $$i=\sqrt{-1}$$
- $\begingroup$ If you have never heard of "complex numbers", the term "real/imaginary component" is useless. Also, $i:=\sqrt{-1}$ is useless if you have not defined the square root function for negative numbers, except if this is just a notational trick, but this is not what you wrote. $\endgroup$M. Winter– M. Winter2020-07-29 20:54:05 +00:00Commented Jul 29, 2020 at 20:54