- #1

NewtonianAlch

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## Homework Statement

Simplify in terms of real and imaginary parts of x and y and sketch them.

1) Re [itex]\frac{z}{z-1}[/itex] = 0

2) I am [itex]\frac{1}{z}[/itex] ≥ 1

## The Attempt at a Solution

1)

[itex]\frac{x + iy}{x + iy -1}[/itex] = 0

Am I allowed to just vanish the imaginary components here and have [itex]\frac{x}{x -1}[/itex]?

If not, I was thinking split up the fraction, and have [itex]\frac{x}{x + iy -1}[/itex] = [itex]\frac{-iy}{x + iy -1}[/itex]

Hence, x = -iy, or x + iy = 0, and for the real component: x = 0

2)

[itex]\frac{1}{x + iy}[/itex] ≥ 1

1 ≤ x + iy where y ≥ 1 for the imaginary component.

I'm not very confident of these answers at all.