Question
Question: The equation \|z – 1\|<sup>2</sup> + \|z + 1\|<sup>2</sup> = 2 represents...
The equation |z – 1|2 + |z + 1|2 = 2 represents
A
A circle of radius 1
B
A 1st. line
C
The ordered pair (0, 0)
D
None of these
Answer
The ordered pair (0, 0)
Explanation
Solution
Sol. \Let z = x + iy " x,yĪR \ |z – 1|2 + |z +1|2 = 2
|x + iy – 1|2 + |x + iy + 1|2 = 2
Ž (x – 1)2 + y2 + (x + 1)2 + y2 = 2
Ž 2x2 + 2y2 + 2 = 2 Ž x2 + y2 = 0
Ž x = 0, y = 0
\ Given equation represent the ordered pair (0,0)