True or false. 1. sqrt 3 + i is a solution of the equation x^3 - 8i=0 2. geometr

Question

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.

Explanation / Answer

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

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