If:
x^5 = 1
find the values of x.
There will be exactly 5 values of x.
Find it with full explanation for a 10th standard student only.
I will give 20 points for it.
_________________________________________________________
Answers
Step-by-step explanation:
Given : x⁵ = 1.
⇒ x = (1)^1/5.
Now, 1 can also be written as,
⇒ 1 = cos 2π + sin 2π.
It can also be written as,
⇒ 1 = cos 2nπ + sin 2nπ
using De Moivre's theorem, we get
⇒ (1)^1/5 = cos(2nπ/5) + i sin(2nπ/5).
The solutions of x⁵ - 1 = 0 can be obtained by putting n = 0,1,2,3,4.
(i) cos(0) + i sin(0) = 1.
(ii) cos(2π/5) + i sin(2π/5)
(iii) cos(4π/5) + i sin(4π/5)
(iv) cos(6π/5) + i sin(6π/5)
(v) cos(8π/5) + i sin(8π/5)
Hope it helps!
Answer:
Step-by-step explanation:
Given : x⁵ = 1.
⇒ x = (1)^1/5.
Now, 1 can also be written as,
⇒ 1 = cos 2π + sin 2π.
It can also be written as,
⇒ 1 = cos 2nπ + sin 2nπ
using De Moivre's theorem, we get
⇒ (1)^1/5 = cos(2nπ/5) + i sin(2nπ/5).
The solutions of x⁵ - 1 = 0 can be obtained by putting n = 0,1,2,3,4.
(i) cos(0) + i sin(0) = 1.
(ii) cos(2π/5) + i sin(2π/5)
(iii) cos(4π/5) + i sin(4π/5)
(iv) cos(6π/5) + i sin(6π/5)
(v) cos(8π/5) + i sin(8π/5)
Hope it helps!