Turn on thread page Beta
    • Thread Starter
    Offline

    1
    ReputationRep:
    Anyone knows how to do it?
    Attached Images
     
    Offline

    1
    ReputationRep:
    |w| = 5, so w must be either 5, -5, 5i, -5i, 3+4i, 3-4i, -3+4i, -3-4i.

    Try each case since there are so few to choose from.
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by JamesF)
    |w| = 5, so w must be either 5, -5, 5i, -5i, 3+4i, 3-4i, -3+4i, -3-4i.

    Try each case since there are so few to choose from.
    Sorry, I dont understand.
    Can you show me how to do it?
    Offline

    2
    ReputationRep:
    (Original post by superkillball)
    Anyone knows how to do it?
    Let w = x + iy

    For the first one w = 4 - 3i
    Offline

    2
    ReputationRep:
    (Original post by JamesF)
    |w| = 5, so w must be either 5, -5, 5i, -5i, 3+4i, 3-4i, -3+4i, -3-4i.

    Try each case since there are so few to choose from.
    Thats only true if the coefficients are integers - in fact there are infinitely many solutions given by the circle in the complex plane radius 5, centre origin
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by It'sPhil...)
    Let w = x + iy

    For the first one w = 4 - 3i
    How come w= 4 - 3i?
    Offline

    2
    ReputationRep:
    (Original post by superkillball)
    How come w= 4 - 3i?
    let w = x + iy
    since lwl = 5, x^2 + y^2 = 25
    so we have l 12 - 9i + x + iyl = 15 + 5 = 20
    so (12 + x)^2 + (y - 9)^2 = 400
    expand and sub x^2 = 25 - y^2
    24x - 18y = 150
    => x = (75 + 9y)/12
    sub into x^2 + y^2 = 25
    ie (after cancelling) y^2 + 6y + 9 = 0
    => (y + 3)^2 = 0
    y = -3 x = 4
 
 
 
Poll
Do you think parents should charge rent?

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

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