# Complex Matchstick puzzle

This is my toughest invention so far, not sure if it's already been done but here it goes.

Move a single stick to obtain a correct equality. (To be clear: the stick needs to be moved and placed down to be part of the new figure; not 'removed').

• Must all numbers be represented as proper Roman or Arabic numerals?
– Sean
Feb 10, 2022 at 17:20
• I'd never seen this before, very clever Feb 10, 2022 at 20:34
• I want to answer, but does a rot13(vardhnyvgl) count? Feb 14, 2022 at 10:49

I believe what you're looking for is this:

where

$$e^{-i\pi}=3-4=-1$$

The title alludes to

the complex number $$i$$ found in the solution.

• Inconsistent that a match is i in one case and 1 in another Feb 11, 2022 at 15:21
• not to be that guy, but technically, no match represents the number 1. the roman numerals are iii and iv. I will grant you that they're still interpreted differently haha Feb 11, 2022 at 16:35
• @juicifer to be fair they're all interpreted as i Feb 11, 2022 at 19:43
• true, but they certainly don't mean the same thing Feb 11, 2022 at 20:19
• @somebody Or rather all interpreted as I (capitalized i). Feb 12, 2022 at 3:42

$$-8^{-iii} = ii-iv$$

• I was really hoping that would be right too but -8^(1/3) = -2, not -8^-3. Feb 10, 2022 at 19:58
• I always intended to start with a bang. How embarrassing for me to have for gotten. Feb 10, 2022 at 20:09

Assuming you have bad stick "handwriting"

This gives you

8-3 = 3 + 2

• I'm finding it difficult to interpret the "-III" as "minus three" instead of "to the negative three" due to its placement in an exponent position Feb 10, 2022 at 23:36
• It's a bit of a stretch, but that was what I was referring to with the bad handwriting comment Feb 10, 2022 at 23:41