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This step is not the source of the fallacy.

This step follows from the previous step (i (i/2 + 3/(2i)) = i( 1/(2i) + 3/(2i)) ) using the distributivity of multiplication over addition: a(b+c) = ab + ac.

Distributivity holds for complex multiplication and addition just the same way as it does for real multiplication and addition; you can prove this by writing out the definitions of complex multiplication and addition.

Why don't you go back to the list of steps in the proof and see if you can identify which one is wrong, now that you know it isn't this one?
This page last updated: May 26, 1998
Original Web Site Creator / Mathematical Content Developer: Philip Spencer
Current Network Coordinator and Contact Person: Joel Chan - mathnet@math.toronto.edu

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