What about plain old
x = -10?-10 ^ 2 = 100
-10 ^ 3 = -1000
-10 ^ 5 = -100000of course, but this problem is solvable without any understanding of complex numbers, and 10*i^2 is a really clunky, multi-operation expression whereas -10 is just an integer.
simplifying one's answers is standard practice and any grader who received the answer in the OP would be obligated to point out that while technically correct, they're missing the basic fact that the answer is -10.
The Rube Goldberg comment is apt as the solution is absurdly complicated and overengineered for the task it performs.
Yeah exactly you're right, why overcomplicate the problem like the Reddit comment did? I guess that's just typical Reddit thinking that being pendantic and using lots of fancy words and long explanations makes you smart.
people being pedantic showoffs doesn't really register as humor for me, TBH
That's true, the OOP is being quite snarky with their comment on a post where someone's had a genuine basic doubt
What an extremely unnecessary explanation. As a math teacher I would have deducted points for this answer.
Unless I was in that clas where we had to write mathematical proofs. I HATED those. Sure, you solved the question but write out this complicated reason for why your answer is the correct answer.
Therefore i¹⁰ = ln(-1)¹⁰/pi¹⁰ = -1
This is true but does not follow from the preceding steps, specifically finding it to be equal to -1. You can obviously find it from i²=-1 but they didn't show that. I think they tried to equivocate this expression with the answer for eiπ which you can't do, it doesn't follow because eiπ and i¹⁰ = ln(-1)¹⁰/pi¹⁰ are different expressions and without external proof, could have different values.
If we know the values of ln(-1)¹⁰ and pi¹⁰ we hypothetically could calculate their divided result as -1 instead of using strict logic, but it is missing a few steps. Moreover logs of negative numbers just end up with an imaginary component anyway so there isn't really any progress to be made on that front. Typing ln(-1)¹⁰ into my scientific calculator just yields i¹⁰pi¹⁰, (I'm guessing stored rather than calculated? Maybe calculated with built in Euler) so the result of division is just i¹⁰ anyway and we're back where we started.
You can find the value of ln(-1)¹⁰ by examining the definition of ln(x): the result z satisfies eᶻ=x. For x=-1, that means the z that satisfies eᶻ=-1. Then we know z from euler's identity. Raise to the 10, and there's our answer. And like you pointed out, it's not a particularly helpful answer.
