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Question

Express :
(a+ib)2aib(aib)2a+ib
in the forum x+iy

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Solution

(a+ib)2aib(aib)2a+ib
=(a+ib)3(aib)3a2+b2
=a3b3i+3aib(a+ib)a3+b3i+3abi(aib)a2+b2
=3abi(a+ib+aib)a2+b2
=6a2bia2+b2
=0+6a2ba2+b2i
Here x=0,y=6a2ba2+b2

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