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Question

State true or false:

(a+ib)2(aib)(aib)2(a+ib)=2b(3a2b2)a2+b2i.

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Solution

(a+ib)2(aib)(aib)2(a+ib)=(a+ib)3(aib)3(aib)(a+ib)
=2(3a2.ib+i3b3)a2+b2=2(3a2bb3)a2+b2i
=2b(3a2b2)a2+b2i.
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