如下,复数计算复数计算(1+√3i)^100+(1-√3i)^100=?(1加根号3乘以i)的100次方加上(1减去根号
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如下,复数计算
复数计算(1+√3i)^100+(1-√3i)^100=?
(1加根号3乘以i)的100次方加上(1减去根号3乘以i)的一百次方=?,i是在根号3外面的
复数计算(1+√3i)^100+(1-√3i)^100=?
(1加根号3乘以i)的100次方加上(1减去根号3乘以i)的一百次方=?,i是在根号3外面的
(1+√3i)^2 = 1-3 + 2√3i = -2 (1-√3i)
(1-√3i)^2 = 1-3 - 2√3i = -2 (1+√3i)
(1+√3i)^3 = -2(1-√3i)*(1+√3i) = -2 * ( 1+4)=-2^3
(1-√3i)^3 = -2(1+√3i)*(1-√3i) = -2 * ( 1+4)=-2^3
因此
(1+√3i)^100+(1-√3i)^100
= (1+√3i)^99*(1+√3i) + (1-√3i)^99*(1-√3i)
= -2^99 * (1+√3i) - 2^99*(1-√3i)
= -2^99 * ( 1+1+√3i-√3i )
= -2^100
(1-√3i)^2 = 1-3 - 2√3i = -2 (1+√3i)
(1+√3i)^3 = -2(1-√3i)*(1+√3i) = -2 * ( 1+4)=-2^3
(1-√3i)^3 = -2(1+√3i)*(1-√3i) = -2 * ( 1+4)=-2^3
因此
(1+√3i)^100+(1-√3i)^100
= (1+√3i)^99*(1+√3i) + (1-√3i)^99*(1-√3i)
= -2^99 * (1+√3i) - 2^99*(1-√3i)
= -2^99 * ( 1+1+√3i-√3i )
= -2^100
如下,复数计算复数计算(1+√3i)^100+(1-√3i)^100=?(1加根号3乘以i)的100次方加上(1减去根号
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复数计算(1+√3i)^100+(1-√3i)^100=?