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ISI Entrance Examination
2019 ISI Entrance Examination
3
ISI 2019 : Problem #3
ISI 2019 : Problem #3
Source: I.S.I. 2019
May 5, 2019
isi
Indian Statistical Institute
complex plane
complex numbers
algebra
Problem Statement
Let
Ω
=
{
z
=
x
+
i
y
∈
C
:
∣
y
∣
⩽
1
}
\Omega=\{z=x+iy~\in\mathbb{C}~:~|y|\leqslant 1\}
Ω
=
{
z
=
x
+
i
y
∈
C
:
∣
y
∣
⩽
1
}
. If
f
(
z
)
=
z
2
+
2
f(z)=z^2+2
f
(
z
)
=
z
2
+
2
, then draw a sketch of
f
(
Ω
)
=
{
f
(
z
)
:
z
∈
Ω
}
f\Big(\Omega\Big)=\{f(z):z\in\Omega\}
f
(
Ω
)
=
{
f
(
z
)
:
z
∈
Ω
}
Justify your answer.
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