JEE MAIN - Mathematics (2019 - 12th April Morning Slot - No. 3)
The equation |z – i| = |z – 1|, i = $$\sqrt { - 1} $$, represents :
a circle of radius 1
the line through the origin with slope – 1
a circle of radius $${1 \over 2}$$
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)
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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