Use a commutative property to complete the statement. ba=
1 answer:
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Answer:
The fifth root is 2[cos(56°) + i sin(56°)]
Step-by-step explanation:
* To solve this problem we must revise De Moiver's rule
- In the complex number with polar form
∵ z = r(cosФ + i sinФ)
∴ z^n = r^n(cos(nФ) + i sin(nФ))
* In the problem
- The fifth root means z^(1/5)
- We can put 32 as a form a^n
∵ 32 = 2 × 2 × 2 × 2 × 2 = 2^5
∴ z = 2^5[cos(280°) + i sin(280°)]
* Lets find z^(1/5)
∴ z^(1/5) = 2[cos(56) + i sin(56)]
* The fifth root of 32[cos(280°) + i sin(280°)] is 2[cos(56°) + i sin(56°)]
Answer:
The distance between the origin and the given point is 13.9283 units.
Step-by-step explanation:
The coordinates of origin are (0,0,0)
We are given a point R(9,7,80
The distance formula:
, where
are coordinates of one point and
are coordinates of other point.
Putting the values as:
We get d =
d =
d = 13.9283
Thus, the distance between the origin and the given point is 13.9283 units.
Answer:
(x - 16)² + (y - 4)² = 8
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (16, 4) and r = 2, thus
(x - 16)² + (y - 4)² = (2 )², that is
(x - 16)² + (y - 4)² = 8