JEE Complex Numbers 2

Algebra Level 5

Let z1,z2z_1,z_2 be complex numbers such that Im(z1z2)=1Im(z_1z_2)=1, the minimum value of z12+z22+Re(z1z2)|z_1|^2+|z_2|^2+Re(z_1z_2) is ω\omega. Then calculate 100ω\lfloor 100\omega\rfloor.

Details and Assumptions

  • Im(z)Im(z) is the imaginary part of complex number zz
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