The identity ( J ) Log[( J + i ) 2 ] = 2 Log( J + i) is

Chapter 0, Problem 3.18

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The identity ( J ) Log[( J + i ) 2 ] = 2 Log( J + i) is valid since Log(( I + i) 2 ] = Log C2i > = In 2 + i ~ and ( J- 7r) 7r 2Log(1 + i) = 2 In 2 + i - =In 2 + i -. 4 2 On chc ocher hand.(2)becauseandLog!(-1+i) 2J=I-2Log(-I +i)Log!(- I + il 2 J = Log( -2i) = In 2 - i :r2( ~ 3:r) 3:r 2 Log( - I + i) = 2 In v 2 + i 4 = In 2 + i T.93While slalcmcnl (I) might he cxpcclcd. we sec that stacemcnc (2) would not beuuc as an cqualily.

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