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

Abhishek Sawant

Abhishek S ( M.Pharm.MBA) tutor for IB/International/IGCSE

Z could be any number
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

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

View 8 more Answers

Related Questions

Give two examples of â??Significant non cash transactionsâ??.
Goodwill written off during the year and depreciation charged on fixed assets
Vidyarajeev
0 0
9
The electrons, which can wander in the solid, are known as __________. (Valence electron, free electron, loosely bound electrons, none of these)
free electrons
Narendra Kumar
0 1
9
What is practical meaning of centre of mass?
The center of mass is the point where all of the mass of the object is concentrated. When an object is supported at its center of mass there is no net torque acting on the body and it will remain in static equilibrium.
Ravi Ranjan
1 0
9
If the ratio of rates of diffusion of two gases is 4:3, then ratio of their molecular weights would be
9:16,rate of diffusion is inversely proportional to molar mass of a gas....
Ayan Arif
The study of the spectrum of characteristic X-rays helps us to __________. (Measure the energy of the incident electrons, measure the wavelength of the incident electrons, measure the energy of the emitted x-rays, identify the element of which the target is made)
D
Narendra Kumar
0 0
6

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

Ask a Question

Related Lessons

Dissolution Of Partnership Firm - Questions
CHAPTER: 5 Q.1 Distinguish between dissolution of partnership and dissolution of partnership firm on the basis of continuation of business. Q.2 Why is Realisation Account prepared on dissolution of partnership...

Mahesh Kumar

1 0
0
Geography Gs & Optional
Earthquakes- Seismic Waves and Internal Structure of the Earth Seismic waves, the waves of energy that travel through the Earth as a result of an earthquake can tell us a lot about the internal structure...

Raghavendra K Ravi

0 0
0
Ratio Analysis
Types of Ratios: Accounting ratio can be classified as Liquidity Ratio Solvency Ratio Activity or Turnover Ratio and Profitability Ratio Liquidity Ratios: It measures short term financial...

Shrimathi Aravind

1 0
0
Basic Accounting Procedures – II Journal
I. Journalise the following Transactions – Chapter 4 (Book Examples) Jan 1, 2004 – Saravanan started the business with Rs. 1,00,000. Jan 3, 2004 – Received cash from Balan Rs. 25,000 Feb...

Alex J

0 0
0
Class 11- Chemistry: Concept Of Aromaticity.
Aromaticity: A compound is said to be aromatic if it follows the following conditions: 1. The molecule is cyclic. 2. The molecule is planar. 3. The molecule is fully conjugated. 4. The molecule has...

Nidhi T.

0 0
0

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 Chennai
Class 12 Tuition in Hyderabad
Class 12 Tuition in Kolkata
Class 12 Tuition in Mumbai
Class 12 Tuition in Pune
Class 12 Tuition in Lucknow
Class 12 Tuition in Noida
Class 12 Tuition in Gurgaon
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