Let w(Im w ≠ 0) be a complex number. Then the set of all complex numbers z satisfying the equation w — barw z = k (1 - z), for some real number k, is :

Question

Let w(Im w ≠ 0) be a complex number. Then the set of all complex numbers z satisfying the equation w — barw z = k (1 - z), for some real number k, is : (A) z: |z| = 1 (B)  z: z = barz  (C)  z: z ≠ 1  (D)  z: |z| =1, z ≠ 1

Tardigrade Admin · Accepted Answer

w- barwz=k-kz kz- barwz=k-w z=(k-w/k- barw) ..........(i) barz=(k- barw/k-w) ..........(ii) (i) Ã (ii) z barz=1 |z|=1 but z≠1

Q. Let $w (I m w \neq = 0)$ be a complex number. Then the set of all complex numbers $z$ satisfying the equation $w — \overset{w}{ˉ} z = k (1 - z),$ for some real number $k$ , is :

$z : ∣ z ∣ = 1$

${z : z = \overset{z}{ˉ}}$

${z : z \neq = 1}$

${z : ∣ z ∣ = 1, z \neq = 1}$

$w - \overset{w}{ˉ} z = k - k z$
$k z - \overset{w}{ˉ} z = k - w$
$z = \frac{k - w}{k - w ˉ} .......... (i)$
$\overset{z}{ˉ} = \frac{k - w ˉ}{k - w} .......... (ii)$
$(i) \times (ii)$
$z \overset{z}{ˉ} = 1$
$∣ z ∣ = 1$
but $z \neq = 1$

Q. Let w(Imw=0) be a complex number. Then the set of all complex numbers z satisfying the equation w—wˉz=k(1−z), for some real number k, is :

z:∣z∣=1

{z:z=zˉ}

{z:z=1}

{z:∣z∣=1,z=1}