What is a Complex Number

[@fayobam_mech_tronics]

Thanks , as a visual person I used to find this hard to visualise!

[@rajanvk939]

Wow just awesome

[@alejndraalmirowitsch4897]

that rotation part is super useful

[@purplrshadowyay]

Or to put it more simply If i = √-1, then i² = (√-1)² = -1

[@stewartmoore5158]

That's putting it more concisely, not simply. You have to do a lot more abstract thinking to understand this set of expressions than the visual guide provided in the short.

[@gerdsfargen6687]

Man this dude is my Maths god!

[@Azooooooooooooz]

Maths? maybe Allaah (God)? no.

[@tornadoruby]

​@@Azoooooooooooozplease don't bring up religions because people are gonna start a war

[@DEVILSWARNING]

@@tornadoruby yea bro these people are very annoying

[@fsponj]

Proof that this dude is a god?

[@Kirmadada2]

​​@@tornadorubythese muslims cant this out of the box out of religion 😂.

[@channel12381]

🎉🎉🎉

[@ionelmiu921]

A complex number is more than representing points in x-y plane. If you only need to represent a point in x-y plane , you don't need imaginary part; enough to have real x and real y axis and, voila, you can represent all the points.

[@c0d3r1f1c]

Yes, but a complex number can be produced by a single function. To describe a 2d output without complex numbers, you need to define 2 functions: one for x and the other for y.

[@suvarthagollamandala8101]

Thank you Sir

[@pinedelgado4743]

Awesome stuff!!

[@ketanmorajker]

That was nice 😮

[@WANEL]

Sqr root of 2 is 1.41 and if sqr root of -4 is 2 cuz sqr cant be negative then sqr root of 1 and -1 is just a bit smaller my house is not 9m and squar of 2 wide but 9 times 1.41

[@pelasgeuspelasgeus4634]

Excuse me, you speak about rotation. Why? Complex numbers are supposed to be points but you treat as if they are vectors. Also, can you graph an equation containing imaginary numbers and show it?

[@pelasgeuspelasgeus4634]

@Paulancar Can you prove that i^0=1? It's an arbitrary convention, right? Can you explain why in all graphs we see the imaginary unit i depicted with same length as the real axis unit? Finally, find the error in the following: -1=i^2=i*i=sqrt(-1)*sqrt(-1)=sqrt((-1)*(-1))=sqrt(1)=1.

[@pelasgeuspelasgeus4634]

@Paulancar Hey buddy. I would appreciate a reply since you appeared so sure on the complex plane.

[@natalia5609]

​@@pelasgeuspelasgeus4634 the "sqrt[(-1)*(-1)=sqrt(-1)*sqrt(-1)" is the error . The identity √(ab)= √a√b holds true only for real numbers, where as in complex number you won't get the same result in LHS and RHS of the identity

[@natalia5609]

​@@pelasgeuspelasgeus4634 And yes i can prove i^0=1 We know i/i =1 (but i by i can be written as i^(1-1) as they have the same base and they are undergoing division) So i^(1-1)=1 => i^0=1 Hence proved

[@natalia5609]

Actually numbers are really fun to play with , one of the reason i love maths

[@NicholsonNeisler-fz3gi]

Someone put circles in my numbers