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Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberGeometric ApplicationMedium2 minPYQ_2022
MathematicsMediumsingle choice

LetS1=z1∈C:z1-3=12andS2=z2∈C:z2-z2+1=z2+z2-1.Then, forz1∈S1andz2∈S2, the least value ofz2-z1is

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Answer:
C
Solution:

Here z1-3=12 represents a circle on argand plane with centre 3,0 and radius 12

Given z2+z2−12=z2−z2+12

⇒z2+z2-1z¯2+z2-1=z2-z2+1z¯2-z2+1

⇒z2z2-1+z2+1+z¯2z2-1+z2+1=z2+12-z2-12

⇒z2+z¯2z2+1+z2-1=2z2+z¯2

⇒ Either z2+z¯2=0 or z2+1+z2-1=2

i.e. z2 lies on imaginary axis or it lies on the line segment joining -1,0 and 1,0

So, the minimum distance between z1 & z2 will be the distance between the points 1,0 & 52,0

Hence, z1-z2min=32

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:Geometric Application
⏱ 2mℹ️ Source: PYQ_2022

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