# Solving an inequality

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#1
Can anyone help solve this inequality? I get stuck at a certain point and don't know what to do next.

Last edited by lamijathepanda; 4 weeks ago
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4 weeks ago
#2
|z-2| is the distance from z to 2. |z+1-i| is the distance from z to 1-i.
|z-2| / |z+1-i| >=1 is the condition that the numerator is >= the denominator.
You can combine these to get the area respresented by the inequality (think geometrically).

For the 2nd inequality, I'm not sure there's a better option that writing z as x+iy and churning through the algebra. It shouldn't be too bad.
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#3
(Original post by DFranklin)
|z-2| is the distance from z to 2. |z+1-i| is the distance from z to 1-i.
|z-2| / |z+1-i| >=1 is the condition that the numerator is >= the denominator.
You can combine these to get the area respresented by the inequality (think geometrically).

For the 2nd inequality, I'm not sure there's a better option that writing z as x+iy and churning through the algebra. It shouldn't be too bad.
Thank you!
0
4 weeks ago
#4
(Original post by lamijathepanda)
Thank you!
Just noticed an error- it should say "...distance to the point i-1" (sign changes).
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