Is this an inconsistency in the foundation of complex numbers?

Asked Mar 21 '20 at 15:29

Active Mar 21 '20 at 15:29

Viewed 51 times

I have always wondered this and apologize if I'm reposting, but I don't know how to find out the answer, also Im a little new to math but always liked it, and I'm learning and am starting out with complex analysis, so here goes. I believe:

$i={\sqrt {-1}} = {\sqrt {\frac{1}{-1}}} = {{\frac{\sqrt {1}}{\sqrt {-1}}}}=\frac{1}{i}$

But that gives you $i^2=1$ and not $-1$. Where did I go wrong?

asked Mar 21 '20 at 15:29

Arjun Verma

8

In $\Bbb C$, it is not true that $\sqrt{a/b}=\sqrt a/\sqrt b$. (In fact your question provides a proof of this fact!) – TonyK Mar 21 '20 at 15:31
3

This one of the most popular duplicates. See also here, or here. – Dietrich Burde Mar 21 '20 at 15:34

Is this an inconsistency in the foundation of complex numbers?

0 Answers0