Harvard Entrance Exam Question | Can you solve?

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ความคิดเห็น • 19

  • @sonicbreaker00
    @sonicbreaker00 12 ชั่วโมงที่ผ่านมา +1

    your answer is one of the infinitely-many values. this is because -1 = exp[i*(pi + 2*pi*n)] where n = ...,-2,-1,0,1,2,...
    therefore, the final answer is exp[i*pi^3/2 (1+2*n)] where n = ...,-2,-1,0,1,2,...

  • @DuncanMaggs
    @DuncanMaggs 17 ชั่วโมงที่ผ่านมา +3

    You need to write the pi symbol more clearly as it often appears as though you are writing the variable x!

  • @naimyadally193
    @naimyadally193 วันที่ผ่านมา +9

    Too slow in writing.😂

    • @MathBeast.channel-l9i
      @MathBeast.channel-l9i  วันที่ผ่านมา +1

      Yeah
      The exponents are in the way that can't be written fast...and it may cause any missunderstanding.

    • @MathBeast.channel-l9i
      @MathBeast.channel-l9i  วันที่ผ่านมา +1

      You can watch it on 2x speed🤗

    • @musicsubicandcebu1774
      @musicsubicandcebu1774 วันที่ผ่านมา

      hold down left click, very useful

    • @xbia1
      @xbia1 วันที่ผ่านมา +1

      It's tedious to write the same expression over and over again.

    • @musicsubicandcebu1774
      @musicsubicandcebu1774 วันที่ผ่านมา

      @@xbia1 I agree, it breaks the flow.

  • @RealQinnMalloryu4
    @RealQinnMalloryu4 ชั่วโมงที่ผ่านมา

    (x ➖ 1pix+1pi).

  • @DanToomey-j8n
    @DanToomey-j8n 21 ชั่วโมงที่ผ่านมา

    -3 y. Course y -1 √>>t =202
    D

  • @SGuerra
    @SGuerra วันที่ผ่านมา +2

    A questão é interessante, mas é preciso especificar melhor até que ponto deve- se resolvê-la. BRASIL Dezembro de 2024.

    • @MathBeast.channel-l9i
      @MathBeast.channel-l9i  22 ชั่วโมงที่ผ่านมา

      Alright Boss 😊
      Thanks for sharing your precious feedback 😌

    • @ddichny
      @ddichny 20 ชั่วโมงที่ผ่านมา +1

      Could have gone straight from 2:52 to 4:46 without losing anyone.

  • @KarlosNeves-v3j
    @KarlosNeves-v3j 4 ชั่วโมงที่ผ่านมา

    😂😂😂

  • @padraiggluck2980
    @padraiggluck2980 4 ชั่วโมงที่ผ่านมา

    cos(π^3/2) + sin(π^3/2)*i ~= (0.7551868,-0.6555097) (together with all z that differ by 2π in the argument)

  • @pelasgeuspelasgeus4634
    @pelasgeuspelasgeus4634 7 ชั่วโมงที่ผ่านมา

    Euler formula is simply wrong. One side is the exp function which tends to infinity and the other side is a sum of 2 trig functions each ranging from -1 to 1, ie it's finite. So, these 2 sides can't be equal.

    • @immovableobjectify
      @immovableobjectify 7 ชั่วโมงที่ผ่านมา

      Euler's equation is well established. When the exponent of e is purely imaginary as it is here, the result has a magnitude of 1, and simply spins around the origin in the complex plane, not tending to infinity. Complex numbers are weird and unintuitive. Imaginary exponents are tough to wrap your head around.

    • @pelasgeuspelasgeus4634
      @pelasgeuspelasgeus4634 6 ชั่วโมงที่ผ่านมา

      @immovableobjectify Euler formula was derived by setting iθ in the exponent Taylor series. Right? But that exp series was validated for real numbers, not for imaginary numbers. So, using it to derive the formula was simply erroneous. And I described why it is erroneous. Try to understand it.