if-arg-z-i-i-2-find-Imz-Rez-

Question Number 146318 by mathdanisur last updated on 12/Jul/21

i f a r g (\frac{z - i}{i}) = 2

f i n d I m z + R e z = ?

Commented by Ar Brandon last updated on 12/Jul/21

- π ⩽ \arg (Z) ⩽ π

Commented by mathdanisur last updated on 12/Jul/21

t h i s i s a n s w e r S e r . ?

Commented by Ar Brandon last updated on 12/Jul/21

No! I just {don}^{'} t understand

your “ 2^{″} since - π ⩽ \arg (Z) ⩽ π

Commented by mr W last updated on 12/Jul/21

n o u n i q u e v a l u e f o r I m z + R e z!

Answered by mr W last updated on 12/Jul/21

l e t z = x + y i

\frac{z - i}{i} = \frac{z i - i^{2}}{i^{2}} = - 1 - z i = - 1 - (x + y i) i

= y - 1 - x i

a r g (\frac{z - i}{i}) = a r g (y - 1 - x i) = 2

y - 1 < 0, x < 0

\frac{- x}{1 - y} = \tan (π - 2)

\Rightarrow y = \frac{x}{\tan (π - 2)} + 1 w i t h x < 0

t h e l o c u s o f z i s t h e l i n e y = \frac{x}{\tan (π - 2)} + 1

w i t h x < 0 .

I m z + R e z = y + x \neq c o n s t a n t

Commented by mathdanisur last updated on 13/Jul/21

T h a n k y o u S e r, a n s w e r : y + x . ?

Commented by mr W last updated on 13/Jul/21

i h a v e s a i d : v a l u e o f x + y i s n o t

u n i q u e!

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