Complex NumbersEasy
Question
The number of complex numbers z such that |z - 1| = |z + 1| = |z - i| equals
Options
A.1
B.2
C.∞
D.0
Solution
Let z = x + iy
|z - 1| = |z + 1| ⇒ Re z = 0 ⇒ x = 0
|z - 1| = |z - i| ⇒ x = y
|z + 1| = |z - i| ⇒ y = - x
Only (0, 0) will satisfy all conditions.
⇒ Number of complex number z = 1
|z - 1| = |z + 1| ⇒ Re z = 0 ⇒ x = 0
|z - 1| = |z - i| ⇒ x = y
|z + 1| = |z - i| ⇒ y = - x
Only (0, 0) will satisfy all conditions.
⇒ Number of complex number z = 1
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