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

Let z = x + i y z - i = z - 1 ⇒ x 2 + ( y - 1 ) 2 = ( x - 1 ) 2 + y 2 ⇒ y = x Hence, the equation represents a line through the origin with slope 1 .

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MathematicsComplex NumberGeometric ApplicationEasy2 minPYQ_2019

MathematicsEasysingle choice

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

Answer:

Solution:

Let $z = x + i y$

$|z - i| = |z - 1| \Rightarrow \sqrt{x^{2} + {(y - 1)}^{2}} = \sqrt{{(x - 1)}^{2} + y^{2}}$

$\Rightarrow y = x$
Hence, the equation represents a line through the origin with slope $1$ .

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:Geometric Application

⏱ 2mℹ️ Source: PYQ_2019

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