Answered

2022-01-17

If $|z-6|<|z-2|$ , what is its solution given given by?

Answer & Explanation

nick1337

Expert

2022-01-17Added 573 answers

Step 1

The inequality is the same as

hence as

Expanding and simplifying we get

that is

So the solutions are all complex numbers whose real part is greater than 4

star233

Expert

2022-01-17Added 238 answers

Step 1

Given

or

alenahelenash

Expert

2022-01-24Added 366 answers

Step 1
$z>4$
detalis
There are 3 cases which are:
First
when $z-6\ge 0$
then $z-2>0$
and
$|z-6|<|z-2|$
becomes
$z-6<z-2$
subtract z gives
$-6<-2$
So $|z-6|<|z-2|$ is true when $z\ge 6$
Second
For $6>z\ge 2$
$|z-6|<|z-2|$
becomes
$6-z<z-2$
$8<2z$
$4<z$
Combining the first two cases $z>4$ and $z\ge 6$
$z>4$
And finally for case three
$z<2$
$|z-6|<|z-2|$
becomes
$6-z<2-z$
add z
$6<2$
which is false

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