Properties of nth Root of a Complex Number
Trending Questions
Q. The nth roots of unity are in
[Orissa JEE 2004]
[Orissa JEE 2004]
- None of these
G.P.
- H.P.
A.P.
Q. If z1, z2, z3.....nn are nth, roots of unity, then for k = 1, 2, ....., n
- |zk+1|=k|zk|
- |zk+1|=|zk|+|zk+1|
- |zk|=|zk+1|
- |zk|=k|zk+1|
Q. α1, α2, α3, ........α100 are all the 100th roots of unity. The numerical value of is
∑∑1≤ i<< j≤ 100(αiαj)5
∑∑1≤ i<< j≤ 100(αiαj)5
- 20
- 0
- none of these
Q. If 1, z1, z2, ..., zn−1 are the roots of zn−1=0, then 13−z1+13−z2+13−z3+...+13−zn−1 is equal to
- n−1∑r=1r⋅3r−1n∑r=13r−1
- n∑r=1r⋅3r−1n∑r=13r−1
- n⋅3n−13n−1−12
- n⋅3n3n−1−12
Q. If α is a non real root of z=(1)1/5, then the value of (1+α+α2+α−2−α−1) is
- 2
- 2α
- −2α4
- α4
Q. Let A1, A2, ⋯, An be the vertices of a regular polygon of n sides in a circle of radius unity and
a=|A1A2|2+|A1A3|2+⋯|A1An|2,
b=|A1A2||A1A3|⋯|A1An|, then ab=
a=|A1A2|2+|A1A3|2+⋯|A1An|2,
b=|A1A2||A1A3|⋯|A1An|, then ab=
Q. If 1, z1, z2, z3, ⋯zn−1 are n roots of unity then the value of 13−z1+13−z2+⋯+13−zn−1 is equal to :
- n⋅3n−13n−1−12
- n⋅3n−13n−1+12
- n⋅3n−13n−1−1
- n⋅3n−13n−1+1
Q. The sum of the roots of equation z6+64=0 whose real part is positive is
- 2√3
- 2
- 4
- √3
Q. If 1, d1, d2, d3⋯, dn−1 be nth roots of unity then which among the following are true
- 11−d1+11−d2+⋯11−dn−1=n−12
- (2+d1)(2+d2)⋯(2+dn−1)=2n+13, if n is odd
- (2−d1)(2−d2)⋯(2−dn−1)=2n−1
- (2+d1)(2+d2)⋯(2+dn−1)=2n+13, if n is even
Q. The value of 6∑k=1(sin2kπ7−cos2kπ7) is
- i
- −1
- −i
- 1