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Math 113 Homework 1 Solutions - Stanford University
math.stanford.edu2 is a cube root of 1 (meaning that its cube equals 1). Proof. We can use the de nition of complex multiplication, we have 1 + p 3i 2! 2 = 1 + p 3i 2 1 + p 3i 2 = 1 4 3 4 + p 3 4 p 3 4! i = 1 2 p 3 2 i = 1 p 3i 2 Thus 1 + p 3i 2! 3 = 1 + p 3i 2 1 p 3i 2 = 1 4 + 3 4 + p 3 4 p 3 4! i = 1 Exercise 1A.10. Find two distinct square roots of i. Proof ...