Q 19 If w=zz-13i and w=1 then z lies on1 a circle - Maths - Complex Numbers and Quadratic Equations

Question

Q   19   I f   w = z z - 1 3 i   a n d   w
= 1   t h e n   z   l i e s   o n 1   a
  c i r c l e              
                 
        2   a n   e l l i p s e 3
  a   p a r a b o l a          
                  4
  a   s t r a i g h t   l i n e

Neha Sethi · Accepted Answer

Dear student
Given: w=1Consider,w=zz-i3Let z=x+iy w=x+iyx+iy-i3w=x+iyx+iy-13w=x+iyx+iy-131=x+iyx+iy-13   as z1z2=z1z2x+iy-13=x+iyx2+y-132=x2+y2     as z=x2+y2x2+y-132=x2+y2y2+19-23y=y219-23y=023y=19y=16
So correct option is 4
Regards

Q 19 . I f w = z z - 1 3 i a n d w = 1 t h e n z l i e s o n 1 a c i r c l e 2 a n e l l i p s e 3 a p a r a b o l a 4 a s t r a i g h t l i n e

$Q 19 . I f w = \frac{z}{z - \frac{1}{3} i} a n d |w| = 1 t h e n z l i e s o n (1) a c i r c l e (2) a n e l l i p s e (3) a p a r a b o l a (4) a s t r a i g h t l i n e$