bookshelf/Bookshelf/Fraleigh/Chapter_1.lean

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import Mathlib.Data.Complex.Basic
/-! # Fraleign.Chapter1
Introduction and Examples
-/
namespace Fraleign.Chapter1
open Complex
open HPow
/-! ## Exercises 1 Through 9
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
_ = 0 + (-1) * I := by simp
end Fraleign.Chapter1