Question

determinati partea imaginara a nr:(1+i)^10+(1-i)^10....

Answer 1

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

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

$=> (1+i)^{10}+(1-i)^{10}=0$

Implicit, partea imaginară este 0..