复数（1+1i）6等于（）A．8B．-8C．8iD．-8i

Question

复数（1+ (1)/(i) ） ⁶ 等于（　　）

A．8

B．-8

C．8i

D．-8i

Answer 1

方法1： (1+(1)/(i) ) 6 = (1+(i)/(i2) ) 6 = (1-i) 6 = [ (1-i) 2 ] 3 = (-2i) 3 =8i ．
方法2： (1+(1)/(i) ) 6 = ((1+i)/(i) ) 6 =((1+i)6)/(i6) =([ (1+i)2 ]3)/(i2) =8i
故选C．