A Sum of Imaginary Powers | Problem 311
Vložit
- čas přidán 8. 09. 2024
- ▶ Greetings, everyone! Welcome to @aplusbi 🧡🤩💗
This channel is dedicated to the fascinating realm of Complex Numbers. I trust you'll find the content I'm about to share quite enjoyable. My initial plan is to kick things off with informative lectures on Complex Numbers, followed by a diverse range of problem-solving videos.
❤️ ❤️ ❤️ My Amazon Store: www.amazon.com...
When you purchase something from here, I will make a small percentage of commission that helps me continue making videos for you. ❤️ ❤️ ❤️
Recently updated to display "Books to Prepare for Math Olympiads" Check it out!!!
❤️ This is Problem 311 on this channel!!! ❤️
🤩 I would consider this a medium problem. What do you think?
🤩 Playlist For Lecture videos: • Lecture Videos
🤩 Don't forget to SUBSCRIBE, hit that NOTIFICATION bell and stay tuned for upcoming videos!!!
▶ The world of Complex Numbers is truly captivating, and I hope you share the same enthusiasm! Come along with me as we embark on this exploration of Complex Numbers. Feel free to share your thoughts on the channel and the videos at any time.
▶ MY CHANNELS
Main channel: / @sybermath
Shorts channel: / @shortsofsyber
This channel: / @aplusbi
Future channels: TBD
▶ Twitter: x.com/SyberMath
▶ EQUIPMENT and SOFTWARE
Camera: none
Microphone: Blue Yeti USB Microphone
Device: iPad and apple pencil
Apps and Web Tools: Notability, Google Docs, Canva, Desmos
LINKS
en.wikipedia.o...
/ @sybermath
/ @shortsofsyber
#complexnumbers #aplusbi #jeeadvanced #jee #complexanalysis #complex #jeemains
via @CZcams @Apple @Desmos @GoogleDocs @canva @NotabilityApp @geogebra
You also could use the fact that the sum of all n-th roots of 1 equals 0, which is also true for the 5-th:
e^(2πi/5) + e^(4πi/5) + e^(6πi/5) + e^(8πi/5)
= -e^(0πi/5) + (e^(0πi/5) + e^(2πi/5) + e^(4πi/5) + e^(6πi/5) + e^(8πi/5))
= -1 + (0)
= -1
I did the same thing. This should have been in video: Third method taking advantage of the circular symmetry!
Nice!
There is a complete visual geometric way: All 4 terms represent vectors (all of lengt 1 and the angles as discussed) in the complex plane. Adding means that you can draw a figure like the famous turtle graphics. This will result in a regular pentagon without the bottom side, i.e. the last point is at -1+0*i = -1
Beautiful. what a simple, geometric proof!
Trigonometry+complexivity😅😂❤
-1
👍😎👏✌️👏😎👍
w = 4 not -1
you have indeterminate form of (z⁵ - 1) / (z - 1) at z = 1
so its limit approaches 5, not 0
z isn't equal 1. z^5 is.
@@vighnesh153 the whole answer is wrong tbh, this video needs a redo
@@TheBlueboyRuhan Could you clarify what part is wrong?