A Locus Problem

Algebra Level 4

Find the locus of a complex number z z satisfying ∣ 2 z − 1 z + i ∣ = 2 \left|\dfrac{2z-1}{z+i} \right |=2 ,

where i = − 1 i=\sqrt{-1} .

Circle Point Straight line Pair of Straigh lines Ellipse

Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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2 solutions

Mvs Saketh
Feb 19, 2015

Straight forward,

take 2 common in numerator Mod,

to get |z-0.5|=|z-(-i)| which is simply the perpendicular bisector of points (0.5,0) and (0,-1)

19 Helpful 0 Interesting 0 Brilliant 0 Confused

Did exactly same.

Gautam Sharma - 6 years, 3 months ago

yeah did the same way

Prakhar Bindal - 5 years, 6 months ago
Niranjan Sai
Mar 12, 2015

It is better to assume z=x+iy and solve the problem them we get the equation 4x+8y+3=0 which is a straight line.

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Ya its traditional.you don't have 5 mins to solve a questions as simple.

Spandan Senapati - 4 years, 3 months ago

It's very time consuming then

Nivedit Jain - 3 years, 7 months ago

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