The equation |z – i| = |z – 1|, i = $$\sqrt { - 1} $$, represents :
JEE · Math · previous-year question
- A.a circle of radius 1
- B.the line through the origin with slope – 1
- C.a circle of radius $${1 \over 2}$$
- D.the line through the origin with slope 1correct
Answer
D. the line through the origin with slope 1
Explanation
Let the complex number z = x + iy Now given | (x + iy) - 1 | = | (x+iy) - i | $$ \Rightarrow $$ (x - 1)2 + y2 = x2 + (y - 1)2 $$ \Rightarrow $$ x = y $$ \therefore $$ the correct answer is option (D)
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