3. Show that quaternion multiplication is associative. That is, show that it is always true that (ξη ) ς =ξ (ης ). Hint: Set 5 = Ço + w etc; and use the formulae in problem 1 to help. Please do not make the mistake of assuming that (ūu) u = ũ (T) without proving it.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.3: De Moivre’s Theorem And Roots Of Complex Numbers
Problem 9E
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How do I prove this quaternion?

3. Show that quaternion multiplication is associative. That is, show that it is
always true that (ξη ) ς =ξ (ης ).
Hint: Set 5 = Ço + w etc; and use the formulae in problem 1 to help. Please do not
make the mistake of assuming that (ūu) u = ũ (T) without proving it.
Transcribed Image Text:3. Show that quaternion multiplication is associative. That is, show that it is always true that (ξη ) ς =ξ (ης ). Hint: Set 5 = Ço + w etc; and use the formulae in problem 1 to help. Please do not make the mistake of assuming that (ūu) u = ũ (T) without proving it.
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