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For any complex number z, the minimum value of | z | + | z – 1 | is (A) 0 (B) 1 (C) 2 (D) –1

For any complex number z, the minimum value of | z | + | z – 1 | is
(A) 0 (B) 1 (C) 2 (D) –1

Grade:

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
Dear student

The answer is option b

Regards
Vikas TU
14149 Points
one year ago
The triangle inequality tells that:
∣z∣+∣z−1∣=∣z∣+∣−(z−1)∣≥∣z−(z−1)∣=∣z−z+1∣=∣1∣=1
⟹∣z∣+∣z−1∣≥1.
So, the minimum value of ∣z∣+∣z−1∣ is 1

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