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Combinatorics Complex number

 
 
ZangZiheng的头像
Combinatorics Complex number
ZangZiheng - 2019年10月20日 Sunday 20:42
 


Combinatorics

 
WangDr. Kevin的头像
Re: Combinatorics Complex number
WangDr. Kevin - 2019年10月28日 Monday 22:05
 

If $a_k$ is $2$ or $4$, $i^{a_k}$ is already a real number.  Since $i^3=-i^1$, the sum is a real number if $1$ and $3$ are paired up.  Thus we can count the following cases on the number of $(1,3)$  pairs: $0$ pairs, $1$ pair, $2$ pairs, $3$ pairs, and $4$ pairs.  Each case is quite straight forward.