First slide

Algebra of complex numbers

Question

For any complex number $z,$ the minimum value of $| z | + | z - 2 i |$ is

Moderate

A

0
B

1
C

2
D

none of these

Solution

We have, for $z \in C$
$| 2 i | = | z + (2 i - z) | \leq | z | + | 2 i - z |$
$\Rightarrow 2 \leq | z | + | z - 2 i |$
Thus, minimum value of $| z | + | z - 2 i | is 2$ and it it attained when $z = i .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App