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Question

Z is rotated through an angle of anticlockwise to get z1 and clockwise to get z2, then

A

, z, are in GP

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B

, z, are in AP

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C

+ = 2 z cos

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D

+ = 2 cos(2 )

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Solution

The correct options are
A

, z, are in GP


C

+ = 2 z cos


D

+ = 2 cos(2 )


We will first find the complex number z1 and z2 using the concept of rotation.

z1z = eiα and z2z = eiα

z1 = zeiα , z2 = zeiα

z1z2 = zeiα × zeiα

z1 ,z ,z2 are in g.p - a

z1 + z2 = zeiα + zeiα

= z ( eiα + eiα )

= z(cosα+isinα+cosαisinα)

= 2zcosα - Option C

z21 + z22 = z2(eiα)2 + z2(eiα)2

= z2(ei2α + ei2α)

= 2 Z2cos 2 α - Option D


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