Home
Class 11
MATHS
If w=z/[z-(1/3)i] and |w|=1, then find ...

If `w=z/[z-(1/3)i]` and `|w|=1,` then find the locus of `z`

Text Solution

AI Generated Solution

To find the locus of the complex number \( z \) given that \( w = \frac{z}{z - \frac{1}{3}i} \) and \( |w| = 1 \), we can follow these steps: ### Step 1: Set up the equation using the modulus condition Since \( |w| = 1 \), we can express this condition as: \[ |w| = \left| \frac{z}{z - \frac{1}{3}i} \right| = 1 \] This implies: ...
Promotional Banner

Similar Questions

Explore conceptually related problems

If omega = z//[z-(1//3)i] and |omega| = 1 , then find the locus of z.

If w=(z)/(z-(1)/(3)i) and |w|=1, then z lies on

If |z-3i|=|z+3i| , then find the locus of z.

If complex number z lies on the curve |z-(-1+i)|=1, then find the locus of the complex number w=(z+i)/(1-i),i=sqrt(-1)1

ABCD is a rhombus in the argand plane.If the affixes of the vertices are z_(1),z_(2),z_(3),z_(4) respectively and /_CBA=(pi)/(3) then find the value of z_(1)+omega z_(2)+omega^(2)z_(3) where omega is a complex cube root of the unity

If w=alpha+i beta, where beta!=0 and z!=1 satisfies the condition that ((w-wz)/(1-z)) is a purely real,then the set of values of z is |z|=1,z!=2( b) |z|=1 and z!=1z=z(d) None of these

If z is a complex number satisfying the equation |z-(1+i)|^(2)=2 and omega=(2)/(z), then the locus traced by omega' in the complex plane is