Which of the following are correct statements concerning the roots of unity? Check all that apply.
2 answers:
Answer:
The correct options are:
A. nth roots of unity are evenly spaced on the unit circle.
B. 1 is always the nth root of unity.
C. The number of nth roots of unity is n.
Step-by-step explanation:
We know that form any complex number 'z' the nth root of unity satisfies the equation:
- Also, the number of nt roots of unity are n.
- Also, 1 is always a root of the equation.
- and -1 is always a root when n is even.
( Since, if we consider,
The roots are:
1,ω,ω² )
- Also, the roots are at a fixed distance or are evenly spaced on a unit circle.
Since they are separated by an angle of:
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Answer:
Part A: The null hypothesis failed to be rejected.
Part B: The null hypothesis failed to be rejected.
Step-by-step explanation:
We have an hypothesis test with null and alternative hypothesis H0: p = 0.5 versus Ha: p > 0.5, which has the test statistic z=1.15.
Part A: If the significance level is 0.05, the conclusion depends on the P-value.
If the P-value is below 5%, the null hypothesis is rejected.
The P-value for this right-tailed tes and z=1.15 is:
The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.
Part B: In this case, the significance level is 0.01 and, as the alternative hypothesis is defined with an unequal sign, the test is two-tailed.
This changes the way we calculate the P-value, as we need to compute the two tails.
The P-value is:
The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis is failed to be rejected.
