Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    2
    ReputationRep:
    a) Given that z = 2 - i, show that z^2 = 3 - 4i.
    b) Hence, or otherwise, find the roots, z1 and z2, of the equation (z+i)^2 = 3 - 4i.
    I got part a right, but can someone teach me how i should start on part b please?
    Offline

    12
    ReputationRep:
    If (z+i)^2= 3-4i then z+i =the roots from part a


    Posted from TSR Mobile
    Offline

    2
    ReputationRep:
    From a we know z+i = sqrt(3-4i) so z+i=+ or - sqrt(3-4i) and hence z+i=+ or -(2-i) which gives you z=2-2i and z=-2

    Hope it helps!
    Offline

    19
    ReputationRep:
    you can do part (a) and you cannot do part (b)? ....
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by TeeEm)
    you can do part (a) and you cannot do part (b)? ....
    yes.
    for part b, i started with (z-i)^2 = 3 - 4i
    2-i = + or - sqrt(3-4i)
    What should i do next? as i dont really get the question. When it said find the roots, does it mean find the square root of 3-4i?
    Offline

    19
    ReputationRep:
    (Original post by alesha98)
    yes.
    for part b, i started with (z-i)^2 = 3 - 4i
    2-i = + or - sqrt(3-4i)
    What should i do next? as i dont really get the question. When it said find the roots, does it mean find the square root of 3-4i?
    teaching till 23.15

    the others above are giving you the correct method
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by TeeEm)
    teaching till 23.15

    the others above are giving you the correct method
    sorry i am learning it myself and i just dont get this type of question, when it asks for the roots. in the case of part b, how does it show 2 - i is the root?
    i am happy to stay till 23,15 to learn FP1, thankyou
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by TeeEm)
    teaching till 23.15

    the others above are giving you the correct method
    hi can someone check my working? i managed to work out the solution

    Since from part a, i can get
    z^2 = 3 - 4i
    z = +or- sqrt (3-4i)
    2-i = +or- sqrt (3-4i)
    sqrt(3-4i) = 2-i or -2+i

    so in part b,
    (z+i)^2 = 3 - 4i
    z+i = +or- sqrt (3-4i)
    z+i = 2-i or -2+i
    z = 2-2i or -2
    Offline

    3
    ReputationRep:
    (Original post by alesha98)
    hi can someone check my working? i managed to work out the solution

    Since from part a, i can get
    z^2 = 3 - 4i
    z = +or- sqrt (3-4i)
    2-i = +or- sqrt (3-4i)
    sqrt(3-4i) = 2-i or -2+i

    so in part b,
    (z+i)^2 = 3 - 4i
    z+i = +or- sqrt (3-4i)
    z+i = 2-i or -2+i
    z = 2-2i or -2
    if z = 2-i
    z^2 = (2-i)^2

    Second part is easy, put some thought into it
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by LelouchViRuge)
    if z = 2-i
    z^2 = (2-i)^2

    Second part is easy, put some thought into it
    (2-i)^2 = (2-i)(2-i), i got this right at the begining
    Offline

    19
    ReputationRep:
    (Original post by alesha98)
    sorry i am learning it myself and i just dont get this type of question, when it asks for the roots. in the case of part b, how does it show 2 - i is the root?
    i am happy to stay till 23,15 to learn FP1, thankyou
    I will write a similar question with a full solution to enlighten you, tomorrow (day off)
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by TeeEm)
    I will write a similar question with a full solution to enlighten you, tomorrow (day off)
    ok thank you so much
    Offline

    19
    ReputationRep:
    (Original post by alesha98)
    ok thank you so much
    let me scan an example I made earlier ...
    different approaches
    Offline

    19
    ReputationRep:
    (Original post by alesha98)
    ok thank you so much
    ..
    Attached Images
      
    Offline

    1
    ReputationRep:
    (Original post by alesha98)
    i dont really get the question. When it said find the roots, does it mean find the square root of 3-4i?
    I think what you were confused about is what a root is? Root just means solution,so it's asking for z, in case you hadn't worked that out yet
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you like to hibernate through the winter months?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.