A complex number z is the said to be unimodular if |z|=1 . Suppose z1 and z2 are complex number such that (z1-2 z2/2-z1 z2) is unimodular and z 2 is not unimodular. Then the point z1 lies on a :

Question

A complex number z is the said to be unimodular if |z|=1 . Suppose z1 and z2 are complex number such that (z1-2 z2/2-z1 z2) is unimodular and z 2 is not unimodular. Then the point z1 lies on a : (A) Straight line parallel to x-axis (B) Straight line parallel to y-axis (C) Circle of radius 2 (D) Circle of radius √2

Tardigrade Admin · Accepted Answer

|(z1-2 z2/2-z1 barz2)|=1 (z1-2 z2)( barz1-2 barz2)=(2-z1 barz2)(2- barz1 z2) |z1|2-2 z1 barz2-2 z2 barz1+4|z2|2 =4-2 barz1 z2-2 z1 barz2 +|z1|2|z2|2 |z1|2|z2|2-|z1|2-4|z2|2+4=0 (|z1|2-4)(|z2|2-1)=0 ⇒ |z1|=2

Q. A complex number $z$ is the said to be unimodular if $∣ z ∣ = 1.$ Suppose $z_{1}$ and $z_{2}$ are complex number such that $\frac{z _{1} - 2 z _{2}}{2 - z _{1} z _{2}}$ is unimodular and $z_{2}$ is not unimodular. Then the point $z_{1}$ lies on a :

Straight line parallel to x-axis

Straight line parallel to y-axis

Circle of radius 2

Circle of radius $2$

Q. A complex number z is the said to be unimodular if ∣z∣=1. Suppose z1​ and z2​ are complex number such that 2−z1​z2​z1​−2z2​​ is unimodular and z2​ is not unimodular. Then the point z1​ lies on a :

Straight line parallel to x-axis

Straight line parallel to y-axis

Circle of radius 2

Circle of radius 2​

Q. A complex number $z$ is the said to be unimodular if $∣ z ∣ = 1.$ Suppose $z_{1}$ and $z_{2}$ are complex number such that $\frac{z _{1} - 2 z _{2}}{2 - z _{1} z _{2}}$ is unimodular and $z_{2}$ is not unimodular. Then the point $z_{1}$ lies on a :

Circle of radius $2$