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(iv)(1)/(i)-(1)/(i^(2))+(1)/(i^(3))-(1)/...

(iv)(1)/(i)-(1)/(i^(2))+(1)/(i^(3))-(1)/(i^(4))=0

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Simplify: (1)/(i)- (1)/(i^(2)) + (1)/(i^(3)) - (1)/(i^(4))

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Prove that: (i) (1-i)^(2)=-2i (ii) (1+i)^(4)xx(1+(1)/(i))^(4)=16 (iii) {i^(19)+((1)/(i))^(25)}^(2)=-4 (iv) i^(4n)+i^(4n+1)+i^(4n+2)+i^(4n+3)=0 (v) 2i^(2)+6i^(3)+3i^(16)-6i^(19)+4i^(25)=1+4i .

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The value of (1 + i)( 1 + i^(2) ) (1 + i^(3)) (1 + i^(4)) is