Fill in the Blank: -
If 'z' lies on a the circle |z|=1; then 2/z lies on _____________ ?

Question

maheshmeghwal9 · Answer

Where, z = a complex number.

maheshmeghwal9 · Answer

z is unimodular.

anonymous · Answer

|z|=1 so we have  $\large z=e^{i \theta} $ and  $\large \frac{2}{z}=2e^{-i \theta} $ now just find  |2/z| to get your answer

ganeshie8 · Answer

2/z lies on circle with |z| = 2 ?

anonymous · Answer

thats right because  |2/z|=2 since $\large \left| \frac{2}{z} \right|=2 \left| e^{-i \theta} \right| =2 $

maheshmeghwal9 · Answer

It is just |2/z| = 2 @mukushla

maheshmeghwal9 · Answer

my book fills the answer with: -

$$\LARGE{Circle}$$

maheshmeghwal9 · Answer

wt should i do?

maheshmeghwal9 · Answer

???????????????????????????????????

ganeshie8 · Answer

it lies on same circle ? or it lies on circle with $\sqrt{2}\ radius\  ?$

maheshmeghwal9 · Answer

i don't know
answer is only circle.

ganeshie8 · Answer

il show my work :

let z = x+iy
|z| = 1 => x^2+y^2 = 1 -----------------(1)
2/z = 2(x-iy)

|2/z| = 2 
=> x^2 + y^2 =2 ----------------------(2)

ganeshie8 · Answer

ack... makes no sense nvm

maheshmeghwal9 · Answer

then $$z'=2z^{-1}$$lies on a circle with radius 2 
i think
so wt answer should be filled up ?

ganeshie8 · Answer

@mukushla

maheshmeghwal9 · Answer

yeah @mukushla ?

anonymous · Answer

well answer is a circle with radius 2

maheshmeghwal9 · Answer

but my book says only

circle

wt should i do?
shall i reject the book's answer????????/

maheshmeghwal9 · Answer

i mean should i?

anonymous · Answer

well thats right ;it does'nt matter to say a circle or a circle with radius 2

anonymous · Answer

am i right guys? or i made a mistake somewhere?

maheshmeghwal9 · Answer

i think right :D

maheshmeghwal9 · Answer

ok thanx for the help everyone:)