分类：教育/科学-学习帮助
问题：数学英语好的来a)1.Ifv=1+iandz=x+iy,fora 
a)1.If v=1+i and z=x+iy,for any real numbers x and yshow that the equatn |z-v|=|vz|Represents a circle.2.find the intersection of the circle in part 1 with the straight line |z-v|=|z+v|.b)Using the roots of z^5=1,or otherwise write z^4+z^3+z^2+z+1 as the product of two qa)1.If v=1+i and z=x+iy,for any real numbers x and yshow that the equatn |z-v|=|vz|Represents a circle.2.find the intersection of the circle in part 1 with the straight line |z-v|=|z+v|.b)Using the roots of z^5=1,or otherwise write z^4+z^3+z^2+z+1 as the product of two quadratic expressions with real coefficientsHence find the exact value of the product cos(2pi/5)cos(4pi/5).
回答：a)1.(x+1)²+(y+1)²=4
2.(-1,1) and (-1,1)

b) (z-1)(z^4+z^3+z^2+z+1)=0
z^4+z^3+z^2+z+1=(z^2-2zcos(2π/5)+1)(z^2-2zcos(4π/5)+1)
=z^4-2z^3(cos(4π/5)+cos(2π/5))+z^2(z+4cos(2π/5)cos(4π/5))-2z(cos(2π/5)+cos(4π/5))+1
1=2+4cos(2π/5)cos(4π/5)
cos(2π/5)cos(4π/5)=-1/4
hint:(z-cis(4π/5))(z-cis(2π/5))(z-cis(-4π/5))(z-cis(2π/5))