The equation of the set of complex number z = x + iy, So that |z – z1| = 5, where z1 = 1 + 2i
(a) x2 + y2 – 2x – 4y – 20 = 0
(b) x2 + y2 + 2x – 4y – 20 = 0
(c) x2 + y2 – 2x + 4y – 20 = 0
(d) x2 + y2 + 2x + 4y + 20 = 0
The correct option (a) x2 + y2 – 2x – 4y – 20 = 0
Explanation:
|z – z1| = 5
∴ |(x + iy) – (1 + 2i)|2 = 25 ---------- z1 = 1 + 2i
∴ |(x – 1) + i(y – 2)|2 = 25
∴ (x – 1)2 + (y – 2)2 = 25
∴ x2 + y2 – 2x – 4y – 20 = 0.
