Question

Describe geometrically the regions of the complex plane given by each of the following sets of
complex numbers:

Answer 1

\[\frac{ \pi }{ 2 }<\arg(\frac{ z-1 }{ z })\le \pi\]

Answer 2

@.Sam.

Answer 3

@smokeydabear

Answer 4

@SerikMB

Your question as stated doesn't really make any senses since z - 1z = z - z = 0.

I'm going to guess that you actually meant z - iz.

Then I'm not sure what you mean by π2 so I'm going to guess that you mean π times 2 which I would usually write as 2π

z - iz = z(1 - i)

Write z in polar form
z = r e^(iθ)

write (1 - i) in polar form
(1 - i) = √2 e^(-iπ/4)

hence
z - iz = r√2 e^i(θ - π/4)

The argument is θ - π/4

Then the requirement is:
2π < θ - π/4 < π

(2+1/4)π < θ < (1+1/4)π
9π/4 < θ < 5π/4

I asked it on yahoo answer. 4u

Answer 5

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