Let zk = cos(2kπ/10) + i sin(2kπ/10); k = 1, 2, ..., 9. List - I List - II<br />(P) For each zk there exists a zj such that zkzj = 1<br />(Q) There exists a k ∈ {1, 2, ..., 9} such that z1z = zk has no solution z in the set of complex numbers<br />(R) |1 - z1||1 - z2|...|1 - z9|/10<br />(S) 1

Let zk = cos(2kπ/10) + i sin(2kπ/10); k = 1, 2, ..., 9. List - I List - II
(P) For each zk there exists a zj such that zkzj = 1
(Q) There exists a k ∈ {1, 2, ..., 9} such that z1z = zk has no solution z in the set of complex numbers
(R) |1 - z1||1 - z2|...|1 - z9|/10
(S) 1 - Σ9k=1 cos(2kπ/10)

Eduprobe

Question:

Let zk = cos(2kπ/10) + i sin(2kπ/10); k = 1, 2, ..., 9. List - I List - II
(P) For each zk there exists a zj such that zkzj = 1
(Q) There exists a k ∈ {1, 2, ..., 9} such that z1z = zk has no solution z in the set of complex numbers
(R) |1 - z1||1 - z2|...|1 - z9|/10
(S) 1 - Σ9k=1 cos(2kπ/10)

Solution:

Question:

Let zk = cos(2kπ/10) + i sin(2kπ/10); k = 1, 2, ..., 9. List - I List - II(P) For each zk there exists a zj such that zkzj = 1(Q) There exists a k ∈ {1, 2, ..., 9} such that z1z = zk has no solution z in the set of complex numbers(R) |1 - z1||1 - z2|...|1 - z9|/10(S) 1 - Σ9k=1 cos(2kπ/10)

Solution:

Let zk = cos(2kπ/10) + i sin(2kπ/10); k = 1, 2, ..., 9. List - I List - II
(P) For each zk there exists a zj such that zkzj = 1
(Q) There exists a k ∈ {1, 2, ..., 9} such that z1z = zk has no solution z in the set of complex numbers
(R) |1 - z1||1 - z2|...|1 - z9|/10
(S) 1 - Σ9k=1 cos(2kπ/10)