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Mathematics
Mathematics
Problem
Let
z
z
z
and
ω
\omega
ω
be complex numbers. If
Re
(
z
)
=
∣
z
−
2
∣
\text{Re}(z) = |z-2|
Re
(
z
)
=
∣
z
−
2∣
,
Re
(
ω
)
=
∣
ω
−
2
∣
\text{Re}(\omega) = |\omega-2|
Re
(
ω
)
=
∣
ω
−
2∣
and
arg
(
z
−
ω
)
=
π
3
\arg(z-\omega) = \frac{\pi}{3}
ar
g
(
z
−
ω
)
=
3
π
, the value of
Im
(
z
+
ω
)
\text{Im}(z+\omega)
Im
(
z
+
ω
)
is a.
1
3
\frac{1}{\sqrt{3}}
3
1
b.
2
3
\frac{2}{\sqrt{3}}
3
2
c.
3
\sqrt{3}
3
d.
4
3
\frac{4}{\sqrt{3}}
3
4
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