if z1,z2 are complex numbers such that |(z1-3z2)+(3-z1z2*)|=1 and |z2| is not equal to 1 then find |z1|{ Here * - Maths - Complex Numbers and Quadratic Equations

Question

if z1,z2 are complex numbers such that |(z1-3z2)+(3-z1z2*)|=1 and
|z2| is not equal to 1 then find |z1|{ Here * means conjugate
of}Experts please don't give links and answer with detailed steps

Ghanshyam Dhakar · Accepted Answer

Dear student,
assume question like z1-3z2/3-z1z¯2 =1z1-3z23-z1z¯2=1z1-3z2 = 3-z1z¯2square on both sidez1-3z22 = 3-z1z¯22z12+3z22-2Re3z1z¯2=32+z1z¯22-2Re3z1z¯2z12+9z22-9-z1z¯22=0use z1z2 = z1z2 and z¯2 = z2z12-z12z¯22+9z22-9=0z12-z12z22+9z22-9=0z121-z22-91-z22=0z12-91-z22=0from question z2≠1then z12-9 =0z1=3 answer
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if z1,z2 are complex numbers such that |(z1-3z2)+(3-z1z2*)|=1 and |z2| is not equal to 1 then find |z1|{ Here * means conjugate of}Experts please don't give links and answer with detailed steps

if z1,z2 are complex numbers such that |(z1-3z2)+(3-z1z2)|=1 and |z2| is not equal to 1 then find |z1|{ Here means conjugate of}Experts please don't give links and answer with detailed steps