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JEE Main 201912 AprilMorning Shift
Exam
JEE Main
Year
2019
Date
12 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Complex Number

JEE Main 2019 · 12 April · Morning Shift · Mathematics · Complex Number

The equation | z - i | = | z - 1 | , i = - 1 , represents:

The equation ∣z−i∣=∣z−1∣,i=−1,| z - i | = | z - 1 | , i = \sqrt{- 1}, represents:The equation | z - i | = | z - 1 | , i = - 1 , represents:

Options

  1. Aa circle of radius 12\dfrac{1}{2}
  2. Ba circle of radius 11
  3. Cthe line through the origin with slope 11
  4. Dthe line through the origin with slope −1- 1

Correct answer

C. the line through the origin with slope 11

Step-by-step solution

The equation | z - i | = | z - 1 | , i = - 1 , represents:

Let z=x+iyz = x + iy

\left|z - i\right| = \left|z - 1\right| ⇒ \sqrt{{x}^{2} + {( y - 1 )}^{2}} = \sqrt{{( x - 1 )}^{2} + {y}^{2}}</p><p></p><p>⇒ y = x<br/>Hence,theequationrepresentsalinethroughtheoriginwithslope<br />Hence, the equation represents a line through the origin with slope1 .

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