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Mathematics
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Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
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EASY
Earn 100
If
Δ
=
6
2
i
3
+
6
12
3
+
8
i
3
2
+
6
i
18
2
+
12
i
27
+
2
i
, then
Δ
is
(a)
an integer
(b)
a rational number
(c)
an irrational number
(d)
an imaginary number
17.07% students
answered this correctly
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Important Questions on Complex Numbers
HARD
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
Let
z
1
and
z
2
be any two non-zero complex numbers such that
3
z
1
=
4
z
2
.
If
z
=
3
z
1
2
z
2
+
2
z
2
3
z
1
then maximum value of
z
is
MEDIUM
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
For all complex numbers
z
of the form
1
+
i
α
,
α
∈
R
,
if
z
2
=
x
+
i
y
,
then
EASY
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
The value of
i
592
+
i
590
+
i
588
+
i
586
+
i
584
i
582
+
i
580
+
i
578
+
i
576
+
i
574
is
EASY
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
The value of
i
18
+
1
i
25
3
is equal to
EASY
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
The value of
-
1
+
i
3
2
n
+
-
1
-
i
3
2
n
where
n
is not a multiple of
3
and
i
=
-
1
,
is
MEDIUM
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
If
z
1
=
2
-
i
and
z
2
=
1
+
i
,
then
z
1
+
z
2
+
1
z
1
-
z
2
+
i
is
MEDIUM
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
If
a
and
b
are unit vectors and
a
+
b
=
1
, then
a
-
b
is equal to.
MEDIUM
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
Let
z
be a complex number such that
z
-
i
z
+
2
i
=
1
and
z
=
5
2
. Then, the value of
z
+
3
i
is
EASY
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
The value of
i
2
n
+
i
2
n
+
1
+
i
2
n
+
2
+
i
2
n
+
3
,
where
i
=
−
1
,
is
MEDIUM
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
If
a
>
0
and
z
=
(
1
+
i
)
2
a
-
i
, has magnitude
2
5
, then
z
-
is equal to:
EASY
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
The modulus of
1
+
i
1
-
i
-
1
-
i
1
+
i
is
EASY
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
If
z
-
α
z
+
α
α
∈
R
is a purely imaginary number and
z
=
2
, then a value of
α
is :
MEDIUM
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
If
a
and
b
are real numbers and
a
+
i
b
11
=
1
+
3
i
,
then
b
+
i
a
11
is equal to
HARD
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
For any real number
r
,
let
A
r
=
e
i
π
r
n
:
n
is a natural number
}
be a set of complex numbers. Then
MEDIUM
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
If
z
and
ω
are two complex numbers such that
z
ω
=
1
and
a
r
g
z
-
a
r
g
(
ω
)
=
π
2
, then:
MEDIUM
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
If
z
is a complex number satisfying
R
e
z
+
I
m
z
=
4
,
then
z
cannot be
HARD
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
If the equation
x
2
+
b
x
+
45
=
0
,
b
∈
R
has conjugate complex roots and they satisfy
z
+
1
=
2
10
,
then
EASY
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
Find the real part of the complex number
1
-
2
i
-
3
MEDIUM
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
Let
z
=
3
2
+
i
2
5
+
3
2
-
i
2
5
.
If
R
z
and
I
z
respectively denote the real and imaginary parts of
z
,
then
MEDIUM
Mathematics
>
Algebra
>
Complex Numbers
>
Introduction to Complex Numbers
The value of sum
∑
n
=
1
13
i
n
+
i
n
+
1
,
where
i
=
-
1
,
equals
