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Question

If a=1+i2, find the value of a6+a4+a2+1

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Solution

a6+a4+a2+1=a4(a2+1)+1(a2+1)=(a2+1)(a4+1)..............eq(1)Here,a=1+i22a=1+iSquaringbothsides,(2a)2=(1+i)22a2=1+2i+i2(i2=1)2a2=2ia4=1(a2+1)(a4+1)=(1+1)(1+1)=0


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