bookshelf/Exercises/Fraleigh/Chapter1.lean

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import Mathlib.Data.Complex.Basic
/-! # Exercises.Fraleign.Chapter1
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Introduction and Examples
-/
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namespace Exercises.Fraleign.Chapter1
open Complex
open HPow
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/-! ## Exercises 1 Through 9
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In Exercises 1 through 9 compute the given arithmetic expression and give the
answer in the form `a + bi` for `a, b ∈ `.
-/
theorem exercise1 : I^3 = 0 + (-1) * I := calc
I^3
= I * (I * hPow I 1) := rfl
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_ = 0 + (-1) * I := by simp
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end Exercises.Fraleign.Chapter1