/sci/ - Science & Math » Thread #11656327

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Tard Sun 10 May 14:31:12 2020 No.11656327 View Reply Original Report

Quoted By: >>11656330 >>11656337 >>11656340 >>11656349 >>11656353 >>11657365 >>11657375 >>11659057 >>11659133

Even though ?(-1) = 1i = i and i^2 = -1,
?(-1) does not equal to i, or rather it is not defined to. Why?

Anonymous

Anonymous Sun 10 May 2020 14:32:49 No.11656330 Report

Quoted By:

>>11656327
Yes.

Anonymous

Anonymous Sun 10 May 2020 14:34:48 No.11656337 Report

Quoted By: >>11656345

>>11656327

because a square root has 2 values

Anonymous

Anonymous Sun 10 May 2020 14:35:00 No.11656340 Report

Quoted By: >>11656564 >>11657457

>>11656327
Why would you think that the square root of -1 is not defined to be i?

Anonymous

Anonymous Sun 10 May 2020 14:37:43 No.11656345 Report

Quoted By:

>>11656337
On your calculator you can toggle between them by using the +/- button. If you have a calculator with the "toggle" functionality.

Anonymous

Anonymous Sun 10 May 2020 14:39:35 No.11656349 Report

Quoted By: >>11656366

>>11656327
Are you taking $-1 \in \mathbb{R}$ or $-1 \in \mathbb{C}$ ? Because $\sqrt{-1}$ only has sense in the latter case.

Anonymous

Anonymous Sun 10 May 2020 14:40:42 No.11656353 Report

Quoted By:

>>11656327
if I really wanted, I could probably cook up some argument why ?1 = 1 makes a bit more sense than -1. ?-1 = i and not -i, on the other hand, is completely arbitrary.

Anonymous

Anonymous Sun 10 May 2020 14:46:59 No.11656366 Report

Quoted By:

>>11656349
Good point.

Anonymous

Anonymous Sun 10 May 2020 16:07:38 No.11656564 Report

Quoted By:

>>11656340
literally every sqt(-1) thread has retards screaming "i^2=-1, but sqrt(-1) doesn't equal i!"
must be a meme from within the math community

Anonymous

Anonymous Sun 10 May 2020 20:10:05 No.11657365 Report

Quoted By:

>>11656327
Because the domain of the square root function is R+

Anonymous

Anonymous Sun 10 May 2020 20:12:55 No.11657375 Report

Quoted By:

>>11656327
Use LaTeX undergrad

Anonymous

Anonymous Sun 10 May 2020 20:49:38 No.11657457 Report

Quoted By:

>>11656340
Cos it could be negative i.

Anonymous

Anonymous Mon 11 May 2020 07:15:04 No.11659057 Report

Quoted By:

>>11656327
"?(-1)" is not actually a well defined object that automatically follows from defining the field extension R(i) with i^2 = -1. It is not meant to be taken literally as "the square root of negative one".

Anonymous

Anonymous Mon 11 May 2020 08:00:14 No.11659133 Report

Quoted By:

>>11656327
Every complex number $z$ outside of $(-\infty, 0]$ has precisely two numbers that when squared give $z$ . One will have positive real part and one will have negative real part. We arbitrarily define the principle branch of the square root function to be the one with positive real part. For -1, there's nothing differentiating i and -i. However, sometimes we define it to be i anyway.

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