计算:(1+i)的五次方?

问题描述:

计算:(1+i)的五次方?

(1+i)^2=1+2i+i^2=2i
(1+i)的五次方=2i*2i*(1+i)=-4-4i

(1+i)²
=1+2i+i²
=1+2i-1
=2i
所以原式=(1+i)²(1+i)²(1+i)
=2i*2i*(1+i)
=-4(1+i)
=-4-4i

:(1+i)的五次方
=(1+i)^4*(1+i)
=[(1+i)^2]^2*(1+i)
=[2i]^2*(1+i)
=-4(1+i)
=-4-4i

(1+i)的五次方
=(1+i)²×(1+i)²×(1+i)
=(1+2i-1)×(1+2i-1)×(1+i)
=(2i)²×(1+i)
=-4(1+i)
=-4-4i