Solving for Roots of Unity Practice Problems Online

What is the complex solution set of the equation $z^4-1=0$ ?

\{1,-1\}

\{i,-1,-i,1\}

\left\{1,\frac{1}{4},\frac{1}{2},\frac{3}{4}\right\}

\left\{\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi\right\}

Which of these is a solution to the equation $z^6=12$ ?

2

我大概[6]\ {12}

\frac{1}{2}+i\dfrac{\sqrt{3}}{2}

-\frac{\sqrt[6]{12}}{2}+i\frac{\sqrt[6]{324}}{2}

Let $U_n$ denote the set of all $n^\text{th}$ roots of unity.

If $U_a=\{yz\mid y\in U_3,\ z\in U_5\}$ , then $a=\ ?$

Which of these is a solution to the following equation?

$x^5+x^4+x^3+x^2+x+1=0$

1

i

\frac{1}{2}+i\dfrac{\sqrt{3}}{2}

\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2}

If $a+bi$ is an $n^\text{th}$ root of unity, then which of these isnot necessarilyan $n^\text{th}$ root of unity?

a-bi

-a-bi

(a+bi)^2

(a+bi)^n

Solving for Roots of Unity