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Z|Z^2|=Z^2 find its all solutions

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SVP
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Joined: 03 Feb 2003
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Z|Z^2|=Z^2 find its all solutions [#permalink] New post 10 Jun 2003, 00:34
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||Z|–Z^2|=Z^2 :stupid2

find its all solutions
SVP
SVP
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Joined: 03 Feb 2003
Posts: 1613
Followers: 5

Kudos [?]: 43 [0], given: 0

Re: PS: MOD3 [#permalink] New post 11 Jun 2003, 07:18
chihao wrote:
stolyar wrote:
||Z|–Z^2|=Z^2 :stupid2

find its all solutions


Answer is 1/2, 0 ?


Alas, you are wtrong. You have lost -1/2.
I have thougnt that such problems are easy, but people do many, many simple mistake by losing or adding roots.
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Re: PS: MOD3 [#permalink] New post 21 Feb 2008, 11:29
||z|-z^2| = z^2
So two cases:
(1) |z|-z^2 = z^2
Again two cases:
(a) z = 2z^2 . Solve to get z = {0,0.5}
(b) z = -2z^2 Solve to get z = {0, -0.5}

(2) |z|-z^2 = -z^2
Solve for z = 0.

All possible roots: z = {-0.5, 0, 0.5}
Re: PS: MOD3   [#permalink] 21 Feb 2008, 11:29
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