Express (a+ib)3/a-ib - (a-ib)3/a+ib in the form a+ib.

a+ib3a-ib-a-ib3a+ib=a+ib4-a-ib4a-iba+ib=a+ib2+a-ib2a+ib2-a-ib2a2-i2b2    Since x+yx-y=x2-y2=a2+i2b2+2aib+a2+i2b2-2iaba+ib+a-iba+ib-a+iba2+b2     Since i2=-1=2a2-b22a2iba2+b2=0+i8aba2-b2a2+b2    ANS...

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