if z1 and z2 are two complex numbers such that |z1-3z2 / 3-z1z2(bar for z2)| = 1 and |z2| not - Maths - Complex Numbers and Quadratic Equations

Question

if z1 and z2 are two complex numbers such that |z1-3z2 / 3-z1z2(bar
for z2)| = 1 and |z2| not equal to 1 fins |z1|

Nagababu Vittam · Accepted Answer

Dear student,if the question is z1-3z23-z1z2¯ =1     and z2≠1                           z1-3z2 =3-z1z2¯                    squaring on both sides                             z1-3z22  =3-z1z2¯2                z1-3z2z1-3z2¯ =3-z1z2¯3-z1z2¯¯                  z1-3z2z1¯-3z2¯ =3-z1z2¯3-z1¯z2z1z1¯ - 3z1z2¯ -3z1¯z2 +9z2z2¯ =9-3z1¯z2- 3z1z2¯ +z1z1¯ z2z2¯             z12-z12 z22 +9z22 -9 =0             z121-z22  -91-z22  =0                            1-z22 z12 - 9 =0       we  know that   z2≠1                                         ∴z12 = 9                                         z1 = 3

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if z1 and z2 are two complex numbers such that |z1-3z2 / 3-z1z2(bar for z2)| = 1 and |z2| not equal to 1 fins |z1|