WBJEE · Maths · Complex Number
For any non-zero complex number \(z\), the minimum value of \(|z|+|z-1|\) is
- A 1
- B \(\frac{1}{2}\)
- C 0
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
\(|z|+|z-1| a\) is complex number \[ \begin{array}{c} |z|+|-(1-z)| \quad|a|=|-a| \\ |z|+|1-z| \quad\{\because|a|=|-a|\} \\ |z|+|1-z| \geq|z+1-z| \\ |z|+|1-z| \geq|1| \\ |z|+|1-z| \geq 1 \\ |z|+|-(z-1)| \geq 1 \\ |z|+|z-1| \geq 1 \end{array} \] Minimum value of \(|z|+|z-1|=1\)
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