Fill in the Blank: - If 'z' lies on a the circle |z|=1; then 2/z lies on _____________ ?
Where, z = a complex number.
z is unimodular.
|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
2/z lies on circle with |z| = 2 ?
thats right because |2/z|=2 since \(\large \left| \frac{2}{z} \right|=2 \left| e^{-i \theta} \right| =2 \)
It is just |2/z| = 2 @mukushla
my book fills the answer with: - \[\LARGE{Circle}\]
wt should i do?
???????????????????????????????????
it lies on same circle ? or it lies on circle with \(\sqrt{2}\ radius\ ?\)
i don't know answer is only circle.
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)
ack... makes no sense nvm
then \[z'=2z^{-1}\]lies on a circle with radius 2 i think so wt answer should be filled up ?
@mukushla
yeah @mukushla ?
well answer is a circle with radius 2
but my book says only circle wt should i do? shall i reject the book's answer????????/
i mean should i?
well thats right ;it does'nt matter to say a circle or a circle with radius 2
am i right guys? or i made a mistake somewhere?
i think right :D
ok thanx for the help everyone:)
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