Let C be the set of complex numbers. If z ∈ C satisfies ∣ z − 3∣ + ∣ z + 1∣ ≥ 8 , find the minimum value of ∣ z − 1∣ .

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MathematicsComplex NumberMiscellaneous/MixedMedium2 minQB

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Let $C$ be the set of complex numbers. If $z \in C$ satisfies $∣ z - 3∣ + ∣ z + 1∣ \geq 8$ , find the minimum value of $∣ z - 1∣$ .

Answer:

Solution:

The boundary is an ellipse centred at 1 with a=4 and c=2. Its semi-minor axis is sqrt(16-4)=2sqrt(3), the required minimum.

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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