24yup manish sir raised a valid point.........
if z1 and z2 are unimodular , then z12 and z22 are also unimodular
so this statement z12+z22=4 cant be true.....
Q
If z1 and z2 r uni modular complex numbers and it is given that z12+ z22=4
then find the value of
(z1+z1)2 +(z2+z2)2
(A)9
(B)10
(C)12
(D)none of these
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24 Answers
1thats quite a long solution!
here how to do it without breaking it into x and y
use this identity
z12 + z22 = z12 + z22
(for unimodular nos)
1no it is possible ,we are talking abt the actual complex nos,not their moduli
for eg take (z1-z2)2 = k -2z1z2,where k = z12+z22
then you get the max possible value of k as 6
24
1hey in d above 1 its Z12 and Z22 but not magnitude of Z12 and magnitude of Z22 na........sooo d condition is satisfied naa??
11sir #20 r u trin to say that it is not possible
but tell me wat to do this 1 then
wats my flaw???
1357All of you are trying to get an answer
but nobody is thinking how z12+z22=4
when z1 and z2 are uni modular
1@manipal.
inequality se value substitute kaise karoge yaar, u don't know what exactly the value is.! and it's not even mentioned in question about taking minimum/maximum value.!
that's why u r getting wrong answer, i guess.!
39usage of am gm in complex numbers, well thats gr8888. i could not think that
11good solution bhargav but i have other plans
z1z1=1
z2z2=1
so we have
z12+1/z12 +2 +z22 +1/z22+2 =L.H.S
8+1/z12 +1/z22
we know that A.M ≥ G.M
so we get
z12 + z12/2≥z1z2
we get
4≥z12z22
and hence we get
8+4/4=9
now our answers r not matching
WHO IS RIGHT THEN???
11hey vivek show ur approach after that
i have a doubt that's y i asked
1haha :D
vivek has already solved it. i'm just having doubt in his solution. asking for a clarification.!
11dude the question is perfect
dont think anything else
try to solve it [1]
1@vivek.
z12 + z22 = 4 => (z1')2 + (z2')2 = 4 !!!?................ (z1' = z1.bar)
how can u conclude the above one !?
is that the method u used to solve or something else ?
11I am not well versed in complex numbers...so this will seem a silly doubt to u.......
The product of two complex numbers is also a complex number
so how is z12+z22=4??