what are The 4-th roots of 1
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= 1
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For 1, the 4 fourth roots are the solutions to x 4-1=0. Factoring yields x 4-1=(x 2-1)(x 2+1)=(x-1)(x+1)(x-i)(x+i) and we get the 4 4th roots of 1 being 1, -1, i, -i. Think of complex numbers as a vector or two dimensional number. Multiplication by i means a rotation of 90 degrees.
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