Question

$<var>(1+i)^{10} + (1-i)^{10}</var>$  Numere complexe. Ce valoare are I?

Answer 1

$(1+i)^2=1+2i+i^2=1+2i-1=2i;\ \ (1-i)^2=-2i$

$(1+i)^{10}+(1-i)^{10}=[(1+i)^2]^5+[(1-i)^2]^5=(2i)^5+(-2i)^5=$

$=(2i)^5-(2i)^5=0$  (-1 la putere impara este tot -1)