nth Root of a Complex Number
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Q. If z1 and z2 are two nth roots of unity, then arg(z1z2) is a multiple of
- nπ
- 3πn
- 2πn
- πn
Q. If z1 and z2 are two nth roots of unity, then arg(z1z2) is a multiple of
- nπ
- 3πn
- 2πn
- πn
Q. If 1, ω, ω2, ω3....., ωn−1 are the n, nth roots of unity, then (1−ω)(1−ω2).....(1−ωn−1) equals
- \N
- 1
- n
- n2
Q. Let z1 and z2 be nth roots of unity which are ends of a line segment that subtend a right angle at the origin. Then n must be of the form
[IIT Screening 2001; Karnataka 2002]
[IIT Screening 2001; Karnataka 2002]
4k + 1
4k + 2
- 4k + 3
- 4k
Q. List I has four entries and List II has five entries. Each entry of List I is to be matched with one entry of List II.
List IList II (A)If x=√6+√6+√6+…up to ∞, then x is equal to(P)4(B)If a and x are positive integers suchthat x<a and √a−x, √x, √a+x(Q)5are in A.P., then least possible value of a is(C)If 3a+2b+4c=0, a, b, c∈R and the line ax+by+c=0 always passesthrough a fixed point (p, q), then thevalue of 2p+q is(R)2(D)If k(sin18 ∘+cos36 ∘)2=5, then thevalue of k is(S)3(T)6
Which of the following is the only CORRECT combination?
List IList II (A)If x=√6+√6+√6+…up to ∞, then x is equal to(P)4(B)If a and x are positive integers suchthat x<a and √a−x, √x, √a+x(Q)5are in A.P., then least possible value of a is(C)If 3a+2b+4c=0, a, b, c∈R and the line ax+by+c=0 always passesthrough a fixed point (p, q), then thevalue of 2p+q is(R)2(D)If k(sin18 ∘+cos36 ∘)2=5, then thevalue of k is(S)3(T)6
Which of the following is the only CORRECT combination?
- C→R;D→S
- C→S;D→T
- C→T;D→R
- C→R;D→P
Q. If 1, ω, ω2, …, ωn−1 are the nth roots of unity of xn=1, then the value of (5−ω)(5−ω2)…(5−ωn−1) is equal to
- 1
- 5n+14
- 4n−1
- 5n−14
Q. The complex number ω which satisfies the equation z3=8i and lying in the second quadrant on the complex plane.
- i−2√3
- 2i−√3
- i−√3
- 2i−3√3
Q. The values of x which satisfies the equation (x−1)3+8=0 are
- −1, 1−2ω and 1−2ω2
- 1, 1+2ω and 1+2ω2
- −1, 1+2ω and 1+2ω2
- 1, 1−2ω and 1−2ω2
