if the roots of the equation z^8=1 are 1,z1,z2,z3,z4,z5,z6,z7, then find the value of sigma k=1 to 7 for z^7K
Answers
Answer:
I __ your questions and my answer of renewable energy sources.
Answer:
Step-by-step explanation:
(z
n
−1)=(z−1)(z−z
1
)(z−z
2
).....(z−z
n−1
)(1)
Differentiating w.r.t. x, and then dividing by (1), we have
z
n
−1
NZ
n−1
=
z−1
1
+
z−z
1
1
+
z−z
2
1
+.....+
z−z
n−1
1
Putting z=3, we get
3
n
−1
n3
n−1
=
2
1
+
3−z
1
1
+
3−z
2
1
+.....+
3−z
n−1
1
⇒
3−z
1
1
+
3−z
2
1
+....+
3−z
n−1
1
=
3
n
−1
n3
n−1
−
2
1
Sorry for some inconvenience as when i inserted it here all get on na ew line .
But looking at the concept wee must understand that in calculating nth roots of unity we knewed one root as 1, rest roots can e calculated in terms cos(theta)+i sin(theta).
That calculation is shown above.
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