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If complex number z satisfies (z- z )^2=12|z|^2-4 then find the maximum value of 3 3 Re (z)+8 Im (z) .

Correct answer

5

Step-by-step solution

aligned & Let z=x+i y z =x-i y & (2 i y)^2=12 (x^2+y^2 )-4 12 x^2+16 y^2=4 & 3 x^2+4 y^2=1 x^2 1 3 + y^2 1 4 =1 & x= 1 3 , y= 1 4 & 3 3 Re (z)+8 Im (z)=3 +4 & =5 & aligned

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