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Exams
Joint Entrance Examination
Mathematics
Complex Numbers
Question 314
Question 314 of 455
Medium
MCQ
For all complex numbers
z
z
z
of the form
1
+
i
α
1+i\alpha
1
+
i
α
,
α
∈
R
\alpha\in\mathbb R
α
∈
R
, if
z
2
=
x
+
i
y
z^2=x+iy
z
2
=
x
+
i
y
, then
A
y
2
−
4
x
+
2
=
0
y^2-4x+2=0
y
2
−
4
x
+
2
=
0
B
y
2
+
4
x
−
4
=
0
y^2+4x-4=0
y
2
+
4
x
−
4
=
0
C
y
2
−
4
x
−
4
=
0
y^2-4x-4=0
y
2
−
4
x
−
4
=
0
D
y
2
+
4
x
+
2
=
0
y^2+4x+2=0
y
2
+
4
x
+
2
=
0
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Official solution
z
2
=
(
1
+
i
α
)
2
=
1
−
α
2
+
2
i
α
z^2=(1+i\alpha)^2=1-\alpha^2+2i\alpha
z
2
=
(
1
+
i
α
)
2
=
1
−
α
2
+
2
i
α
, so
x
=
1
−
α
2
,
y
=
2
α
x=1-\alpha^2,\ y=2\alpha
x
=
1
−
α
2
,
y
=
2
α
. \[y^2+4x-4=4\alpha^2+4(1-\alpha^2)-4=0.\]
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