Q.

Consider a 'n'  sided regular polygon A1,A2,.....An  having it’s center at origin. If 'z1' represents the vertex A1 then complex number representing the vertex that is adjacent to A1,  are:

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a

± z1e2πin

b

± z1eiπn

c

z1e±i2πn

d

None

answer is C.

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Detailed Solution

Vertices adjacent to z1 are z2 and zn Now z2z1=1⇒z2z1=e2πi/n⇒z2=z1e2πi/nAlso z1zn=1⇒z1zn=e2πi/n⇒z1=zne2πi/n
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Consider a 'n'  sided regular polygon A1,A2,.....An  having it’s center at origin. If 'z1' represents the vertex A1 then complex number representing the vertex that is adjacent to A1,  are: