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(Solved): Establish that whenever b,c, and d are real numbers satisfying b^(2)+c^(2)+d^(2)=1, then the quatern ...



Establish that whenever

b,c

, and

d

are real numbers satisfying

b^(2)+c^(2)+d^(2)=1

, then the quaternion

q=bi+cj+dk

has the property that

q^(2)=-1

; hence, there are infinitely many quaternions whose squares equal -1 .



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