UrbanPro
Login Ask & Answer Success Stories Paid Courses Free Classes Tuition & Classes Fees Write a Review All Categories Help Center
Post your Learning Need Signup as a Tutor
✕

Popular Cities

Bangalore

Hyderabad

Delhi

Mumbai

Chennai

Pune

Kolkata

Gurgaon

Ahmedabad

Jaipur

Noida

✕

Take Class 12 Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Book a Free Demo

Class 12 Tuition > Learn Class XI-XII Tuition (PUC) > Find the complex number z |z+2| > |z-3|
✕

Search in

Find the complex number z |z+2| > |z-3|

Asked by Last Modified  

10 Answers

Learn Class XI-XII Tuition (PUC)

Follow 0
Answer

Please enter your answer

Tutor

Z could be any number
Comments
Dislike Bookmark

Simply Re(z) is less than 1/2. Either use z = x + iy and solve. Or simply use the concept of perpendicular bisector.
Comments
Dislike Bookmark

Re(z) is less than 1/2. Either substitute z = x + iy and solve. Or use the concept of perpendicular bisector.
Comments
Dislike Bookmark

Tutor

Let z=x+iy |z+2| = sqrt ((x+2)^2+y^2) squaring both sides |z+2|^2 = (x+2)^2+y^2 Similarly |z-3|^2 = (x-3)^2+y^2 To find, when (x+2)^2 > (x-3)^2 as y^2 gets cancelled. Simplifying, 4x+4>-6x+9 10x>5 x>1/2 and y can take any value.
Comments
Dislike Bookmark

Lecturer in Mathematics in IIT level, 22 years experience and qualification M.Sc(Maths)

x> 1/2.
Comments
Dislike Bookmark

IIT Educated and well experienced experts selecting only a few highly motivated and ambitious students

Since z=x + yi is the kind of complex number we are looking out for ....therefore we substitute this in the given inequality. | (x+yi) + 2 | > | (x+yi) - 3 | | (x+2) + yi | > | (x-3) + yi | But | x + yi | = sqrt (x^2 - y^2), applying this we get sqrt > sqrt squaring both sides we get (x+2)...
read more
Since z=x + yi is the kind of complex number we are looking out for ....therefore we substitute this in the given inequality. | (x+yi) + 2 | > | (x+yi) - 3 | | (x+2) + yi | > | (x-3) + yi | But | x + yi | = sqrt (x^2 - y^2), applying this we get sqrt [ (x+2) ^2 - y^2 ] > sqrt [ (x-3)^2 - y^2 ] squaring both sides we get (x+2) ^2 - y^2 > (x-3)^2 - y^2 (x+2) ^ 2 - (x-3) ^ 2 > 0 (x + 2 + x - 3) (x + 2 - x + 3) > 0, since a^2 - b^2 = (a+b)(a-b) (2x - 1)(5) > 0 (2x - 1) > 0 x > (1/2) Hence all complex numbers of the form z=x + yi, with x > 0.5 satisfy the given inequality, note that y can also take negative real values and I have therefore ignored the case z=x - yi. Geometrically this means , z is such a complex number such that its distance from the point (-2,0) is greater than its distance from the point (3,0). If you should draw a number line and locate these points, its clear that all z with x > 0.5 satisfy the condition. Such numbers lie to the right of the vertical line passing through x = 0.5. read less
Comments
Dislike Bookmark

Expert In Our Work

|z+2| it is the distance of pt. z from pt (-2,0) in the complex plane and |z-3| represent the distance of pt. z from (3,0) in the complex plane. now you know what is mode of a complex no. represent . to solve this type of question you have to first identify the region to find the region you have to...
read more
|z+2| it is the distance of pt. z from pt (-2,0) in the complex plane and |z-3| represent the distance of pt. z from (3,0) in the complex plane. now you know what is mode of a complex no. represent . to solve this type of question you have to first identify the region to find the region you have to replace inequality sign with equality sign first . i.e |z+2|=|z-3| say it equation -(a ) if you sea in your notes this is the equation bisector of fixed pt.(-2,0)and (3,0) so the locus of z is a line which is perpendicular bisector of line joining pt (-2,0) &(3,0) so we get a line from equation (a) now we have to find z(in other words we have to find region where z lies because inequalities always satisfies a region) region in this question is the values of z which satisfies the inequality.first perpendicular bisector is passes through (-0.5,y) in the complex plane.so the z is any complex no .whose real part is fixed i.e -0.5 but imaginary part can take any value on imaginary axis say k where k belongs to (-infinity ,+infinity). i hope you understand .please sea your notes also while study this. read less
Comments
Dislike Bookmark

D=WT/VOL
Comments
Dislike Bookmark

A true teacher of Science and Math

I dint get answer from anyone, two complex no never compare
Comments
Dislike Bookmark

Trainer

I x +iy +2 I > I x +iy -3 I Sqrt((x+2)^2 +y^2) > Sqrt((x-3)^2 +y^2) I After simplification you can obtain x > 1/2
Comments
Dislike Bookmark

View 8 more Answers

Related Questions

What is the best to solve first order differential equations?
The best method is direct integration.
Raju P
Will NCERT sufficient for inorganic chemistry?
Add PRADEEP or TRUEMAN's guide
Ravi Ranjan
What is the difference between nuclear fission and nuclear fusion?
Webster's New World defines fusion as "melting together." Therefore, nuclear fusion is the process by which more than one nuclei join together to form a heavier nucleus. Nuclear fusion is the process that...
Sugantha
I have experience of teaching as a tutor, but I never taught online. Now I do not have much time to go to student's home; those are far from my residence. I have laptop and internet available almost all the time. What else (software and hardware) do I need for online tutoring?
Skype, teamviewer
Kamlesh
8. The maximum signaling rate which can be transmitted along a channel is numerically equal to _________. a. Twice the channel bandwidth b. Less than the channel bandwidth c. The channel bandwidth d. None of the above
twice the channel bandwidth
Narendra Kumar

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

How to Pass Entries under GST Regime?
How to Pass Entries under GST Regime: Under the new GST Regime all these taxes (excise, VAT, CST, Service tax, Entry Tax) will get subsumed into one account and assesse will get benefit of setting of...

FR Prashanth Reddy

Types of Banks-HSC,Class 12-OC & Economics,Class 11 Business Studies
What are various types of banks?

Rajiv Vadera

1 0
0
Integration Formulas
A

Amrtha S.

0 0
0
CORRECT TECHNIQUE = 1ST STEP TOWARDS SUCCESS
CHEMISTRY The main problem among students is fear, when they start studying chemistry from class IX actually. Unfortunately the curriculum in all boards is designed in such a way, that the basic concepts...

Dr. Anirban Chakraborty

0 0
0
GST News, Notifications And Announcements
Central Tax Notifications: Composition Scheme- Notification 3 & 8/2017: Composition scheme threshold has been notified to be 75 lakhs (earlier recommended only). This will be beneficial to small...

FR Prashanth Reddy

Recommended Articles

Meet Mohammad Wazid, a skilled trainer for...

Mohammad Wazid is a certified professional tutor for class 11 students. He has 6 years of teaching experience which he couples with an energetic attitude and a vision of making any subject easy for the students. Over the years he has developed skills with a capability of understanding the requirements of the students. This...

Read full article >

Meet Raghunandan.G.H, a B. Tech Tutor from...

Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...

Read full article >

Meet Swati, a Hindi Tutor from Bangalore

Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...

Read full article >

Meet Radhe Shyam Burman, an MBA Tutor from...

Radhe Shyam is a highly skilled accounts and finance trainer with 8 years of experience in teaching. Accounting is challenging for many students and that’s where Radhe Shyam’s expertise comes into play. He helps his students not only in understanding the subject but also advises them on how to overcome the fear of accounts...

Read full article >

Find Class 12 Tuition near you
Class 12 Tuition in Delhi
Class 12 Tuition in Bangalore
Class 12 Tuition in Hyderabad
Class 12 Tuition in Kolkata
Class 12 Tuition in Mumbai
Class 12 Tuition in Chennai
Class 12 Tuition in Pune
Class 12 Tuition in Lucknow
Class 12 Tuition in Jaipur
Class 12 Tuition in Noida
Online Tuition Class 12

Looking for Class 12 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you
X

Looking for Class 12 Tuition Classes?

The best tutors for Class 12 Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class 12 Tuition with the Best Tutors

The best Tutors for Class 12 Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more

ThinkVidya Learning Pvt Ltd © 2010-2025All Rights Reserved