JEE Advanced | 2013Complex NumbersHard
Question
Let complex numbers α and 
lie on circles (x - x0)2 + (y - y0)2 = r2 and (x - x0)2 + (y - y0)2 = 4r2 respectively. If z0 = x0 + iy0 satisfies the equation 2|z0|2 = r2 + 2, then |α| =
lie on circles (x - x0)2 + (y - y0)2 = r2 and (x - x0)2 + (y - y0)2 = 4r2 respectively. If z0 = x0 + iy0 satisfies the equation 2|z0|2 = r2 + 2, then |α| = Options
A.
B.
C.
D.
Solution
Given : α satisfies |z - z0| = r ⇒ |α - z0 | = r ..........(1)
satisfies |z - z0| = 2r 
.........(2)squaring (1) and (2) we get
⇒
..........(3)&
⇒
⇒
⇒ 1+ 2 |z0|2 - 2 - |α|2 - |z0|2 + |z0|2 |α|2 = 8|z0|2 |α|2 - 8|α|2
⇒ -1 + |z0|2 - 7|z0|2 |α|2 + 7|α|2 = 0
⇒ (|z0|2 - 1) (7|α2|- 1) = 0
⇒ |z0| = 1 (rejected as r = 0)
&
Create a free account to view solution
View Solution FreeMore Complex Numbers Questions
The value of (−i)−117 is -...If represents a pair of intersecting lines with angle of intersection ′θ′ then the value of |A| is...If z1 & z2 are two complex numbers & if arg but |z1 + z2| ≠ |z1 - z2| then the figure formed by the points represe...For two unimodular complex numbers z1 and z2, if A = and B = , then A-1.B-1 is equal to -...Let i = . The product of the real part of the roots of z2 - z = 5 - 5i is -...