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Algebra Level 3

Find the value of x x such that ∑ n = 1 x ( n i n ) = 2000 + 2001 i \displaystyle \sum_{n=1}^x ( n i^n) = 2000 + 2001 i .

Notation: i = − 1 i = \sqrt{-1} is the imaginary unit .


The answer is 4001.

Mark Vincent Esmeralda Mamigo by Mark Vincent Esmeralda M… , 24

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1 solution

Xiangchen Kong
Dec 30, 2015

since imaginary number is in a loop of 4:(i ，-1，-i , 1).We can easily get the value of each loop:2-2i So we need 1000 loops to complete the value(2000-2000i),therefore 4000 items are included. Besides we add another one:4001 into the loop ,we can get 2000+2001i .

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