Question

For any complex number $z$ the minimum value of $|z|+|z-2013i|$ is...

• A. $2010$
• B. $2011$
• C. $2013$
• D. $2012$

Answer 1

Answer: (C)

$2013$

Q:- minimum value of $\left|z\right|+|z-2013i|$

Solution For ZEG

$\left|2013i\right|=|z+(2013i-z\left)\right|⩽\left|z\right|+|2013i-z|$

$\Rightarrow 2013⩽\left|z\right|+|z-2013i|$

$\Rightarrow$ minimum value of $\left|z\right|+|z-2013i|$ is

2013

which is attained when $z=i$

so, c is correct option.

$x^2+y^2⩽1$ & $y^2⩽1-x.$