Powers of i, with a System of Equations?!?

[Josh0Pascual]

About the author

Hey, my name is Josh. I recently graduated 8th grade and I am going into High School, and I am extremely interested in Math. I have just finished Algebra-2 and I am going to take Pre-Calculus this year.

Quick Summary

The thing that I want to show is that you can evaluate “i”(imaginary unit) to any power using a system of equations. Those two things might sound completely unrelated, but I managed to find a connection between the two. My intention is for the audience of this video to better visualize imaginary numbers in a different way that they haven’t been introduced to before. The derivation of the whole formula is just extremely satisfying to break down.

Target medium

I’m looking for a collaborator that can make me a 3blue1brown style video animation on this discovery that I have made.

More details

I haven’t exactly written about this anywhere online because I didn’t really want other people stealing my ideas, so I made my own private Desmos link on it Here

Contact details

The best way to contact me is through my phone number because I do not receive Discord notifications. i’ll put my Discord @ and my phone number though. Reach me through my phone number first please.

Phone: 704-685-1334

Discord: @! Soulute.-TG Jack#5891

Additional context

(Is there any other relevant information? Additional sources pertinent to the discussion?)

(Any additional licensing information? If you do not say anything, this post will be considered CC-BY.)

[SimonAndreys]

Don't be afraid that someone steals your idea ! By putting them online, you'll get feedback from other math enthusiasts, validation and criticism and you'll improve your knowledge and skills. During my phd I made the mistake not to talk about my ideas (not because I was afraid of stealth but because I thought they were not good enough) and as a consequence I lost a lot of time on misconceptions that could've been clarified with a simple discussion with another mathematician. Share your ideas early and you'll grow as a mathematician and have lots of other new and relevant ideas. If you cling to them you may very well stop your growth.

[Josh0Pascual]

Don't be afraid that someone steals your idea ! By putting them online, you'll get feedback from other math enthusiasts, validation and criticism and you'll improve your knowledge and skills. During my phd I made the mistake not to talk about my ideas (not because I was afraid of stealth but because I thought they were not good enough) and as a consequence I lost a lot of time on misconceptions that could've been clarified with a simple discussion with another mathematician. Share your ideas early and you'll grow as a mathematician and have lots of other new and relevant ideas. If you cling to them you may very well stop your growth.

I put the desmos link in the comment and you can input the number that you’re raising “i” to the power of and it will give you the value of it in the form of coordinates on the plane. that’s what I want a content producer for so I can make this into a 3blue1brown style video.

[LaruelleG]

It's really interesting to see young people get interested in this kind of thing, especially if you're barely into high school. I am not familiar with your country's (seems to be the US from the way you talk), so I don't really know what things like "algebra 2" mean. However, I would recommend that you also get an "expert" (for this kind of work, graduate students would also do) involved. They could shed light on some things you might have missed, or know a theorem or an easier way to prove something in your approach etc. best of luck !

[LaruelleG]

your country's *education system, sorry.

[Josh0Pascual]

It's really interesting to see young people get interested in this kind of thing, especially if you're barely into high school. I am not familiar with your country's (seems to be the US from the way you talk), so I don't really know what things like "algebra 2" mean. However, I would recommend that you also get an "expert" (for this kind of work, graduate students would also do) involved. They could shed light on some things you might have missed, or know a theorem or an easier way to prove something in your approach etc. best of luck !

Thanks So basically, the levels of math in the US are like this: Pre-Algebra (8th Grade Level) Algebra 1 (9th Grade Level) Geometry (10th Grade Level) Algebra 2 (10th/11th Grade Level) Pre-Calculus (11th/12th Grade Level) Calculus 1,2 and 3. (12th Grade/College Level)

The education system in the US is not very good but I managed to get around that by watching 3blue1brown videos.

I really want to find someone who can make me a video on this thing that I made so I can submit it to the SoME2, I have a serious passion for math and I want to have a chance at winning.

Do you know where to find a content producer?

[LaruelleG]

It's really interesting to see young people get interested in this kind of thing, especially if you're barely into high school. I am not familiar with your country's (seems to be the US from the way you talk), so I don't really know what things like "algebra 2" mean. However, I would recommend that you also get an "expert" (for this kind of work, graduate students would also do) involved. They could shed light on some things you might have missed, or know a theorem or an easier way to prove something in your approach etc. best of luck !

Thanks So basically, the levels of math in the US are like this: Pre-Algebra (8th Grade Level) Algebra 1 (9th Grade Level) Geometry (10th Grade Level) Algebra 2 (10th/11th Grade Level) Pre-Calculus (11th/12th Grade Level) Calculus 1,2 and 3. (12th Grade/College Level)

The education system in the US is not very good but I managed to get around that by watching 3blue1brown videos.

I really want to find someone who can make me a video on this thing that I made so I can submit it to the SoME2, I have a serious passion for math and I want to have a chance at winning.

Do you know where to find a content producer?

Unfortunately I don't, otherwise I would not be looking for one myself ^^. best of luck !

[SimonAndreys]

It looks like people how can make animations are the scarce resource here ! I considered learning to use manim but I've not even managed to install the library for now. I've had a look at your desmos link, I'm not really sure of what is your system of equations. I might not have understood but I gather that your theorem is that for any real number p, i^p=x+iy where x and y satisfy the following system of equations : x^2+y^2=1 and y=tan(90 p) (angle in degree units). That's impressive coming from an 8th grader but it's rather straightforward for someone having enough familiarity with complex numbers. But you might have something new in the way you explain it. I think that the crux of the question is : how do you define a non-integer power of i ? If you have an insightful take on this question this may make a nice video.

[elancha98]

I hate to be that guy, but nonintegers powers of an imaginary number are not well defined... This is because the complex logarithm is a multivaluate function.

However, i find that this is quite impressive specially coming from an undergraduate and I think there is a lesson of discovery and it will make an interesting video. I don't have a lot of experience with video editting and that stuff but i manage (more or less) my way around manim. I don't have an american phone number so I will get in touch with you through discord to see if you are interested. In any case do not be afraid of sharing your ideas no matter how stupid or great you think they are. The mathematical community is (in general, there are always exceptions everywhere) a very helpfull, kind and trustworthy community.

Keep up the work!

[Josh0Pascual]

I hate to be that guy, but nonintegers powers of an imaginary number are not well defined... This is because the complex logarithm is a multivaluate function.

However, i find that this is quite impressive specially coming from an undergraduate and I think there is a lesson of discovery and it will make an interesting video. I don't have a lot of experience with video editting and that stuff but i manage (more or less) my way around manim. I don't have an american phone number so I will get in touch with you through discord to see if you are interested. In any case do not be afraid of sharing your ideas no matter how stupid or great you think they are. The mathematical community is (in general, there are always exceptions everywhere) a very helpfull, kind and trustworthy community.

Keep up the work!

Thank you so much bro I appreciate you so much man. You are the best. what is your Discord so I can contact you?

[Josh0Pascual]

I hate to be that guy, but nonintegers powers of an imaginary number are not well defined... This is because the complex logarithm is a multivaluate function.

However, i find that this is quite impressive specially coming from an undergraduate and I think there is a lesson of discovery and it will make an interesting video. I don't have a lot of experience with video editting and that stuff but i manage (more or less) my way around manim. I don't have an american phone number so I will get in touch with you through discord to see if you are interested. In any case do not be afraid of sharing your ideas no matter how stupid or great you think they are. The mathematical community is (in general, there are always exceptions everywhere) a very helpfull, kind and trustworthy community.

Keep up the work!

What’s your Discord user ID so I can contact you?