一个关于高级函数的题.The solutions of the equation z^4+4(z^3)i-6z^2-4zi-i=0 are the vertices of a convex polygon in the complex plane.What is the area of the polygon?
问题描述：
一个关于高级函数的题.
The solutions of the equation z^4+4(z^3)i-6z^2-4zi-i=0 are the vertices of a convex polygon in the complex plane.What is the area of the polygon?
答
该多边形的面积为2倍的2的4次方根,或32的4次方根,2^(5/4).由z^4+4(z^3)i-6z^2-4zi-i=0 得(z+i)^4=1+i.设w=z+i,则方程化为w^4=1+i,再设w=p(cosa+isina),则(p(cosa+isina))^4=√2(cos45+isin45),其中w的模p=2的开8次方...