#Russian grade 8, olympiad math problem. translated with cambridge translator.

17 messages · Page 1 of 1 (latest)

versed hinge
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i dont undertand it at all..

According to legend, the Pythagorean, Hippasus, who unveiled the concept of irrational numbers during a maritime expedition, was cast overboard by his peers "for introducing an element of the universe that contravenes the doctrine that all entities within the cosmos can be reduced to whole numbers and their relationships." Two millennia later, a similar fate befell complex (imaginary) numbers, which were first articulated by the Italian mathematician Cardano. He posited that "these intricate magnitudes are devoid of utility, albeit remarkably clever." Complex numbers can be expressed utilizing the so-called imaginary unit i, which satisfies the equation: i^2 = -1. Like real numbers, the imaginary unit can engage in arithmetic operations. For instance: (1 + 5i)^2 = 1 + 10i + (5i)^2 = 1 + 10i - 25. Based on this premise, please consolidate the equivalent expressions from the following lists: A) (3+2i)(3-2i) B) (1+i)^3 C) x^2-2x+4 ext{ at } x=1+i D) ext{sqrt}{4-13} Option 1) 2 Option 2) 3i Option 3) 13 Option 4) 2i - 2.

latent tinselBOT
rugged nexus
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we assume there exists a number called i, and its property is that i^2 = -1

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with that we can use it in regular arithmetic operations as the example there shows

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what is it that you are struggling with, exactly?

lyric dragon
versed hinge
versed hinge
versed hinge
rugged nexus
upper spearBOT
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artemetra

rugged nexus
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and sqrt is $\sqrt{4-13}$

upper spearBOT
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artemetra

tender pecan
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Привет, тебе ещё нужна помощь в этой задаче?

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Тут всё не так сложно:

  1. (3+2i)(3-2i) это формула сокращённого умножения - разность квадратов. Выражение ты представляешь, как 3² - (2i)², 3² = 9, а (2i)² = 4i², так как i² = -1, то 4i² = 4 * i² = 4 * -1 = -4 следовательно исходное выражение равно:
    3² - (2i)² = 9 - (-4) = 9 + 4 = 13; то есть для варианта A ответ 3
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Если этот вопрос ещё является актуальным, то напиши сюда или мне в лс. Я отвечу по возможности