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# complex number questions I dunno about watch

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1. 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
2. does anyone know how to do these kind of questions?
3. 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).
4. so what start with (3-2i) = z-i ?
5. I dont see why you would square root each side
6. would you get z-i-3=0
7. I really dont understand this at all, anyone care to shine some light for me?
8. Let's say that . This means that you have and , and because , you can say that , which you need to solve for .

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9. 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?
10. this is really frustrating, unless im being a total idiot I cant find my mistake
11. anyone?
12. are you sure the answers in the back of the book aren't : 3+i, 3-i
13. 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.
14. 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?
15. anyone again?
16. alright.....
17. (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.
18. omg thank you very much for all ur guys help I reli appreciate it alot

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