复数z=(1-i)^10*(3-4i)^2/(-√3+i)^8的模为

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复数z=(1-i)^10*(3-4i)^2/(-√3+i)^8的模为
复数z=(1-i)^10*(3-4i)^2/(-√3+i)^8的模为

复数z=(1-i)^10*(3-4i)^2/(-√3+i)^8的模为
(1-i)²
=1-2i-1
=-2i
所以(1-i)^10=-32i^5=-32i
(3-4i)²
=9-24i-16
=-7-24i
-√3+i
=1/2(cos5π/6+isin5π/6)
所以(-√3+i)^8=(1/256)(cos20π/3+isin20π/3)
=(1/256)(-√3+i)/2
所以z=-32i|-7-24i|/(1/512)(-√3+i)
|z|=32*25/(1/256)
=204800

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