Math miscellaneousHard
Question
If |z-4| < |z-2|, its solution is given by
Options
A.Re(z) > 0
B.Re(z) < 0
C.Re (z) > 3
D.Re(z) > 2
Solution
Given | z - 4 | < | z - 2 | Let z = x + iy
⇒ |(x-4) + iy)| < |(x-2) + iy| ⇒ (x -4)2 + y2 < (x - 2)2 + y2
⇒ x2 - 8x + 16 < x2 - 4x + 4 ⇒ 12 < 4 x ⇒ x > 3 ⇒ Re(z) > 3
⇒ |(x-4) + iy)| < |(x-2) + iy| ⇒ (x -4)2 + y2 < (x - 2)2 + y2
⇒ x2 - 8x + 16 < x2 - 4x + 4 ⇒ 12 < 4 x ⇒ x > 3 ⇒ Re(z) > 3
Create a free account to view solution
View Solution FreeMore Math miscellaneous Questions
If the system of linear equations x + ky + 3z = 0 3x + ky - 2z = 0 2x + 4y - 3z = 0 has a non-zero solution (x, y, z), t...If a, b, c are in A.P., b, c, d are in G.P. & c, d, e are in H.P., then -...Line drawn perpendicular to plane x + 2y - 3z = 21 at point A meets plane 2x + ky + 5z = 8 at point B. If mid point of A...The coefficient of x13 in the expansion of (1 - x)5 (1 + x + x2 + x3)4 is :-...The image of the point (-1, 3, 4) in the plane x - 2y = 0 is...