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Mathematics 20 Online
OpenStudy (maheshmeghwal9):

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

OpenStudy (maheshmeghwal9):

Where, z = a complex number.

OpenStudy (maheshmeghwal9):

z is unimodular.

OpenStudy (anonymous):

|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 (ganeshie8):

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

OpenStudy (anonymous):

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

OpenStudy (maheshmeghwal9):

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

OpenStudy (maheshmeghwal9):

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

OpenStudy (maheshmeghwal9):

wt should i do?

OpenStudy (maheshmeghwal9):

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

ganeshie8 (ganeshie8):

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

OpenStudy (maheshmeghwal9):

i don't know answer is only circle.

ganeshie8 (ganeshie8):

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 (ganeshie8):

ack... makes no sense nvm

OpenStudy (maheshmeghwal9):

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

ganeshie8 (ganeshie8):

@mukushla

OpenStudy (maheshmeghwal9):

yeah @mukushla ?

OpenStudy (anonymous):

well answer is a circle with radius 2

OpenStudy (maheshmeghwal9):

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

OpenStudy (maheshmeghwal9):

i mean should i?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (maheshmeghwal9):

i think right :D

OpenStudy (maheshmeghwal9):

ok thanx for the help everyone:)

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