计算:(-2根号3 +i)/(1+2根号3i) +(根号2/1-i)^2010的值为?
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计算:(-2根号3 +i)/(1+2根号3i) +(根号2/1-i)^2010的值为?
答案是2i,我算了i+1
答案是2i,我算了i+1
![计算:(-2根号3 +i)/(1+2根号3i) +(根号2/1-i)^2010的值为?](/uploads/image/z/7800236-44-6.jpg?t=%E8%AE%A1%E7%AE%97%3A%28-2%E6%A0%B9%E5%8F%B73+%2Bi%29%2F%281%2B2%E6%A0%B9%E5%8F%B73i%29+%2B%EF%BC%88%E6%A0%B9%E5%8F%B72%2F1-i%EF%BC%89%5E2010%E7%9A%84%E5%80%BC%E4%B8%BA%3F)
逐项进行计算
-2根号3+i/(1+2根号3i)
=(-2√3 + i)(1 - 2√3i) / 13
=i
(根号2/(1+i))^2010
= ((1 - i) / √2) ^ 2010
= (-i) ^ 1005
= - i ^ 1005
=-i
所以,原式=i-i=0
-2根号3+i/(1+2根号3i)
=(-2√3 + i)(1 - 2√3i) / 13
=i
(根号2/(1+i))^2010
= ((1 - i) / √2) ^ 2010
= (-i) ^ 1005
= - i ^ 1005
=-i
所以,原式=i-i=0
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