A halloween equation

outubro 30, 2021 § Deixe um comentário

The following little equation appeared in a debate among some friends. It concerned the possibility of a result such as -1 = 1. The culprit was:

-1 = i * i

One of the friends answered the question as:

-1 = √-1 * √-1

-1 = √1

-1 = 1

What is the problem with the above spooky answer? Well, the way I see it, this friend had one little mistake, which was to consider the equation inside the Cartesian plane. In my opinion, it is clearly under the Argand plane, which contains the complex numbers (e.g., x+yi). In this case, we could not consider i = √-1 but i = √1 and the negative sign should be outside both square roots.  Hence, the answer would be:

-1 = – (√1 * √1)

-1 = -√1

-1 = -1

I guess the only spooky math around should be the Halloween challenges, like the one below.

Font: mashupmath

Notice that it takes two black cats to make one pumpkin. So:

Black Cat = 6

Cauldron = 14

Pumpkin = 12

Happy Halloween, folks. A nice trick-or-treating to you all.

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