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Question
Simplify the following:
i i2 i3 ... i2000
Sum
Solution
= `"i"^(1 + 2 + 3 + 2000)`
∵ `1 + 2 + 3 ....... "n" = ("n"("n" + 1))/2`
= `"i"((2000 xx 2001)/2)`
= `"i"^((1000 xx 2001))`
= `["i"^1000]^2001`
= `"i"^2001000`
= 1
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Introduction to Complex Numbers
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