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complex number questions I dunno about watch

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    Heres the question I've spent an hour on and cant get the answer in the back of the book which is 3-i, -3+3i btw

    Verify that (3-2i)^2 = 5-12i. And find the two roots of the equation
    (z-i)^2 =5-12i

    I have verified that they are the same but dont know how to find the two factors

    Any1s help is greatly appreciated, lols thanks
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    does anyone know how to do these kind of questions?
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    If (3-2i)^2 = 5 - 12i and (z - i)^2 = 5 - 12i then you can say (3 - 2i)^2 = (z - i)^2; square root each side (not forgetting the plus/minus thingy).
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    so what start with (3-2i) = z-i ?
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    I dont see why you would square root each side
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    would you get z-i-3=0
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    I really dont understand this at all, anyone care to shine some light for me?
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    Let's say that y = 5 - 12i. This means that you have (3-2i)^2 = y and (z-i)^2 = y, and because y = y, you can say that (3 - 2i)^2 = (z - i)^2, which you need to solve for z.

    Spoiler:
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    |3-2i| = |z-i| \Rightarrow 3 - 2i = z - i\ \mbox{or}\ 3 - 2i = i - z
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    yeah but I cant seem to get the right answer tho, can someone show me how you do it because I cant see where my maths is going wrong?
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    this is really frustrating, unless im being a total idiot I cant find my mistake
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    anyone?
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    are you sure the answers in the back of the book aren't : 3+i, 3-i
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    Expand (z-i)^2 =5-12i and then rearrange it so you get a quadratic equal to 0.

    You can then find the roots of the equation by using the quadratic formula.
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    yes the answers in back of the book are fine but I cant get the ruddy answers tho, Ive tried using the quadratic formula but cant get it right please can someone show me how to do it?
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    anyone again?
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    alright.....
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    (Original post by Soloman)

    Verify that (3-2i)^2 = 5-12i. And find the two roots of the equation
    (z-i)^2 =5-12i
    If (3-2i)^2 = 5-12i then it's also true that (-3+2i)^2=5-12i.

    Can you see why?

    From this you can see that z-i=3-2i or z-i=-3+2i. Make z the subject in those little equations and you're finished.
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    omg thank you very much for all ur guys help I reli appreciate it alot
 
 
 
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