Homework SourseTrue or false 1 sqrt 3 i is a solution of the equation x3
True or false.
1. sqrt 3 + i is a solution of the equation x^3 - 8i=0
2. geometrically, the ninth roots of many complex number z are equally spaced around the unit circle centered at the origin.
True or false.
1. sqrt 3 + i is a solution of the equation x^3 - 8i=0
2. geometrically, the ninth roots of many complex number z are equally spaced around the unit circle centered at the origin.
1. sqrt 3 + i is a solution of the equation x^3 - 8i=0
2. geometrically, the ninth roots of many complex number z are equally spaced around the unit circle centered at the origin.
Solution
1). to check root or not of x^3 -8i=0
plug x= sqrt(3) +i
(sqrt(3) +i)^3 -8i=0
sqrt(3)^3 + i^3 +3sqrt(3)^2 . i + 3.sqrt(3) .i^2 -8i=0
3sqrt(3) -i +3.3i -3sqrt(3) -8i=0
-i +9i -8i=0
9i-9i=0
0=0
so yes sqrt(3) + i is a solution of x^3 -8i=0
True
2)
is also True
