- #1

- 17

- 0

## Homework Statement

Determine the region in the complex plane described by |z-2i| < |z+ i|

## Homework Equations

z= x+ iy

|z|= (x

^{2}+ y

^{2})

^{1/2}

## The Attempt at a Solution

|z-2i| < |z+ i|

|z-2i|/|z+ i| < 1

|z-2i| = [(x-2i)

^{2}+ y

^{2}]

^{1/2}

|z+ i| = [(x+i)

^{2}+ y

^{2}]

^{1/2}

[(x-2i)

^{2}+ y

^{2}]

^{1/2}

--------------- < 1

[(x+i)

^{2}+ y

^{2}]

^{1/2}

[(x-2i)

^{2}+ y

^{2}]

^{1/2}*[(x+i)

^{2}- y

^{2}]

^{1/2}

---------------------------------- < 1

[(x+i)

^{2}+ y

^{2}]

^{1/2}*[(x+i)

^{2}- y

^{2}]

^{1/2}

Am I on the right track of solving this so far? If so how do I proceed to the next step? If not what part did I do wrong? Any feedback is appreciated!