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Q.

If 3z+i2z+34i=32  , then locus z represent i= 1  and zC  

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a

parabola 

b

straight line

c

circle

d

half of plane

answer is A.

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Detailed Solution

after simplifying we get z+ i 3 = z+ 3 2 2i  
Pz   is equidistant from  A 0, 1 3  and B  
3 2 ,2   thus locus of z is straight line   
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If 3z+i2z+3−4i=32  , then locus z represent i= −1  and z∈C