Question

求(1+i)^100+(1-i)^100的实部、虚部、模、辐角主值及共轭复数。（求详细解题思路）

如题 在线等

Answer 1

(1+i)^100=[(1+i)⁴]^25
={[(1+i)²]²}^25
=[(2i)²]^25
=(-4)^25
=-4^25
(1-i)^100=[(1-i)⁴]^25
={[(1-i)²]²}^25
=[(-2i)²]^25
=(-4)^25
=-4^25
(1+i)^100 +(1-i)^100
=-4^25 -4^25
=-2×4^25
=-2^51
(1+i)^100 +(1-i)^100的实部为-2^51,虚部为0.
-2^51表示负的2的51次方.