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Question

Let z=x+iy be a complex number such that |z|=1, where i=1. Match List - I with List - II.

List-IList - II(I)Re(iz1+z2) is equal to(P) 0(II)Im(iz1+z2) can be equal to(Q) 1(III)Number of integers NOT in the(R) 12range of Im(iz1+z2) is equal to(IV)12πarg(iz1+z2) is equal to(S)12(whereπ<arg(z)π)(T)14(U) 14

Which of the following is only CORRECT combination?

A
IP,Q
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B
IP,Q,R
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C
IIQ, R, S
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D
IIIQ, R
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Solution

The correct option is C IIQ, R, S
|z|=11z=¯z

Now iz1+z2=iz+1z=iz+¯z

=i2 cos θ=(12 sec θ)i

Re(iz1+z2)=0 and Im(iz1+z2)=12 sec θ

So, the range of imaginary part iz1+z2 is (,12][12,)

iz1+z2 is purely imaginary

arg(iz1+z2)=π2 or π2

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