Question

show that 1+i^10+i^100-i^1000=0
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Answer 1

Step-by-step explanation:

i^10=[i^2]^5=-1

i^100=[i^2]^50=1

i^1000=[i^2]^500=1

so, LHS= 1+i^10+i^100+i^1000

             =  1+[-1]+1-[1]

              =1-1+1-1 =0 =RHS