Question

复数（-1+i）的n次方和（-1-i）的n次方,表示成三角函数的形式是什么,一样么?

Answer 1

-1+i=√2[cos(3π/4)+isin(3π/4)]

(-1+i)^n=(√2)^n[cos(3nπ/4)+isin(3nπ/4)]

-1-i=√2[cos(5π/4)+isin(5π/4)]

(-1-i)^n=(√2)^n[cos(5nπ/4)+isin(5nπ/4)]