Establish associative law of multiplication

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The discussion focuses on establishing the associative law of multiplication for complex numbers, specifically through the lens of absolute values and arguments. The equation z1(z2z3)=(z1z2)z3 is examined, emphasizing the need to demonstrate that both magnitudes and arguments behave associatively. Participants agree that the solution involves multiplying out the expressions and confirming their equivalence. It is clarified that the magnitudes multiply while the arguments add, reinforcing the associative property. Overall, the conversation highlights the mathematical principles underpinning the associative law in complex multiplication.
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Homework Statement


Establish associative law of multiplication by considering absolute values and arguements.
z1(z2z3)=(z1z2)z3


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The Attempt at a Solution


I think I need to use r(costheta +isintheta)
r1(costheta1+isintheta1)[r2r3(costheta2+isintheta2)(costheta3+isintheta3)]=
Is this just a bunch of multiplying out and showing it's the same?
 
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Yes. The magnitudes multiply and the arguments add. Both operations are associative.
 
Ok, I think I see.
 

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