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We know -1=-1, make these two into different but equivalent fractions -1/1=1/-1, take the square root of both sides sqrt(-1/1)=sqrt(1/-1), the rule sqrt(x/y)=sqrt(x)/sqrt(y) is true so we can write... sqrt(-1)/sqrt(1)=sqrt(1)/sqrt(-1), simplify the fractions i/1=1/i, multiply both sides by i -1/1=i/i, i/i=1 and -1/1 is -1 so we can write... -1=1 There's your proof i=sqrt(-1) spoiler:i is imaginary

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16y ago

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