18 lines
385 B
Plaintext
18 lines
385 B
Plaintext
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/-
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# References
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1. Fraleigh, John B. A First Course in Abstract Algebra, n.d.
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-/
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import Mathlib.Data.Complex.Basic
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open Complex
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open HPow
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-- In Exercises 1 through 9 compute the given arithmetic expression and give the
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-- answer in the form $a + bi$ for $a, b ∈ ℝ$.
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theorem ex1_1 : I^3 = 0 + (-1) * I := calc
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I^3
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= I * (I * hPow I 1) := rfl
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_ = 0 + (-1) * I := by simp
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