- #1

alexcc17

- 48

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## Homework Statement

Determine the interior, the boundary and the closure of the set {z ε: Re(z

^{2}>1}

Is the interior of the set path-connected?

## Homework Equations

Re(z)=(z+z*)/2

## The Attempt at a Solution

Alright so z

^{2}=(x+iy)(x+iy)=x

^{2}+2ixy-y

^{2}

so Re(x

^{2}+2ixy-y

^{2})= x

^{2}-y

^{2}>1

So would the image be a hyperbola that starts when each axis is >1 leaving a hole in the center?

Boundary: {z ε: Re(z

^{2}=1}

Interior: none

Closure: {z ε: Re(z

^{2}>1}

Since there is no interior the question of interior path connectedness is mout.

I'm not sure if this is right though