Question

For any complex number z, maximum value of $|z| - |z - 1|$ is

• A. 0
• B. 1
• C. 3/2
• D. None of these

Answer 1

Answer: (B)

1

Answer 2

Sol. We know that $|z_{1} - z_{2}| \geq |z_{1}| - |z_{2}|$

$\mathbf{\therefore|z| - |z - 1| \leq |z - (z - 1)|}$ or $\mathbf{|z|}\mathbf{-}\mathbf{|z}\mathbf{-}\mathbf{1|}\mathbf{\leq}\mathbf{1}$,

$\mathbf{\therefore}$ Maximum value of $\mathbf{|z|}\mathbf{-}\mathbf{|z}\mathbf{-}\mathbf{1|}$is 1