Complex NumbersHard
Question
The equation |z - i| + |z + i| = k, k > 0, can represent
Options
A.an ellipse if k > 2
B.line segment if k = 2
C.an ellipse if k = 5
D.line segment if k = 1
Solution
Put z = x + iy
if k > 2 ⇒ ellipse
if 0 < k < 2 ⇒ hyperbola
if k = 2 ⇒ x2 = 0
⇒ |y - 1| + |y + 1| = 2
⇒ -1 ≤ y ≤ 1
Hence z = x + iy lies on line segment joining - i and i
if k > 2 ⇒ ellipse
if 0 < k < 2 ⇒ hyperbola
if k = 2 ⇒ x2 = 0
⇒ |y - 1| + |y + 1| = 2
⇒ -1 ≤ y ≤ 1
Hence z = x + iy lies on line segment joining - i and i
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