Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

If |z-4|<|z-2| then find its solution ?

1 Answer

Mar 25, 2018

$x > 3$ $x > 3$

Explanation:

Assuming $z = x + i y$ $z = x + i y$ we have

$\sqrt{{(x - 4)}^{2} + y^{2}} < \sqrt{{(x - 2)}^{2} + y^{2}}$ $sqrt((x-4)^2+y^2) < sqrt((x-2)^2+y^2)$ and squaring

${(x - 4)}^{2} + y^{2} < {(x - 2)}^{2} + y^{2}$ $(x-4)^2+y^2 < (x-2)^2+y^2$ or

$- 8 x + 16 < - 4 x + 4 \Rightarrow x > 3$ $-8x+16 < -4x + 4 rArr x > 3$

Related questions

Impact of this question

959 views around the world

You can reuse this answer
Creative Commons License