We have to evaluate the fourth roots of unity.
For each natural number say 'n', there are exactly 'n' nth roots of unity which is expressed in the form as
where k=0,1,2,.... n-1
Since we have to evaluate the fourth root of unity.
Therefore, we take k=0,1,2,3 and n=4
So, we get
Now, For k=0, we get our first root as:
First root = 1
Now, for k=1, we get
(Eulers Formula)
So,
So, second root = i
Now, for k=2, we get
(Eulers Formula)
So,
Third root = -1
Now, for k=3, we get
(Eulers Formula)
So,
So, fourth root = -i
Hence, all the fourth roots of unity are 1, i, -1 and -i
Therefore, option D is correct as all the given roots in option A, B and C are the fourth roots of unity.
Answer:
13
Step-by-step explanation:
Let PS = x and RP = x-5
Using Pythagorean theorem on the two smaller rt triangles formed,
6^2 + x^2 = (ST)^2
6^2 + (x-5)^2 = (RT)^2
Now use Pythag on big triangle and sub in above values:
(2x-5)^2 = 6^2 + x^2 + 6^2 + (x-5)^2
Multiply out and simplify to
x^2 - 5x -36 = 0
Factor the quadratic: ((x-9)(x+4)=0 Therefore x=9 or x=-4. We may disregard the negative answer so x = 9. So PS is 9 and RP is 4.
Therefore entire hypotenuse is 4 + 9 or 13.
No you can’t write 0.02 as tenths as it is in the ones place
Answer:
the answer is 3/8 or if you want the answer in a decimal its 0.375
Step-by-step explanation:
HOPE THIS HELPS!!