Minimum value

Example. 

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

a) 0

b) 1

c) 2

d) none of these.

Solution.

We have for z \in C, |2i|=|z+(2i-z)|\leq |z|+|2i-z|

\Longrightarrow 2 \leq |z|+|z-2i|

Thus, the required minimum value is 2 and it is attained for any z lying on the segment joining z=0 and z=2i.

Answer. Option C.

More later,

Nalin Pithwa

This entry was written by Nalin Pithwa, posted on August 2, 2015 at 8:13 am, filed under Cnennai Math Institute Entrance Exam, Complex Numbers, IITJEE Mains, ISI Kolkatta Entrance Exam and tagged . Bookmark the permalink. Follow any comments here with the RSS feed for this post. Post a comment or leave a trackback: Trackback URL.

Leave a Reply

Fill in your details below or click an icon to log in:

Gravatar
WordPress.com Logo

You are commenting using your WordPress.com account. ( Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. ( Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. ( Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. ( Log Out /  Change )

w
Cancel

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: