cOmPlEx NuMbErS

thats 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)

no 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

yup 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.....

hey in d above 1 its Z₁² and Z₂² but not magnitude of Z₁² and magnitude of Z₂² na........sooo d condition is satisfied naa??

sir #20 r u trin to say that it is not possible

but tell me wat to do this 1 then
wats my flaw???

chiiiiiiiii yes sir right..... excellent point

usage of am gm in complex numbers, well thats gr8888. i could not think that

good 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???

not at all a long solution..this was easy answer is 12

oh.! thanx buddy :)

dude the question is perfect
dont think anything else

try to solve it [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 ?

yes u r right

any real no x can be written in the form x = x + i0