Complex Numbers Test

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Complex Numbers Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

2√-9,√−16, is equals to

A
48

B
24

C
-48

D
-24
Question 2
1 / -0

The expression (1 + i)²ⁿ+ (1 - i)²ⁿ, n ∈ N, is

A
a purely imaginary number

B
a purely real number

C
a non-real complex number

D
a complex number in which real and imaginary parts are equal
Question 3
1 / -0

Which one of the following equations has the root a ± b?

A
x² - 2ax + b² = 0

B
(a²+ b²)x² - 2ax + b = 0

C
x² - 2ax + a² - b² = 0

D
2a²x² - x + a²+ b² = 0
Question 4
1 / -0

If w is the complex cube root of unity, then {(a + b w + c w² )/(c + a w + b w²)} + {(c + a w + b w² )/(a + bw + cw²)} + {(b + cw + aw²)/(b + cw + aw ²)} =

A
1

B
w

C
w²

D
0
Question 5
1 / -0

If z₁andz₂ are non real complex numbers such that z₁+z₂andz₁z₂ are real numbers , then

A
z1=z2

B
z1=z1 and z2=z

C
z1=−z2

D
none of these
Question 6
1 / -0

If (-1 + √ 3i)ⁿ+ (-1 - √ 3i)ⁿ= 2ⁿα, then α is equal to

A
2

B
-1

C
2 or -1

D
None of these
Question 7
1 / -0

The smallest positive integer n for which (1+i/(1- i))ⁿ=1 is

A
2

B
4

C
8

D
16
Question 8
1 / -0

If │z-12/z - 8i│= 5/3 and Re (z) = 6, then Im (z) =

A
8

B
17

C
8 or 17

D
None of these
Question 9
1 / -0

Amp ( -1 - i) is

A
π/4

B
-π/4

C
-3 π/4

D
3 π/4

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Complex Numbers Test - 3

Result

Complex Numbers Test - 3

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Rank

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SHARING IS CARING

Question 1

48

24

-48

-24

Question 2

a purely imaginary number

a purely real number

a non-real complex number

a complex number in which real and imaginary parts are equal

Question 3

x2 - 2ax + b2 = 0

(a2 + b2)x2 - 2ax + b = 0

x2 - 2ax + a2 - b2 = 0

2a2x2 - x + a2 + b2 = 0

Question 4

1

w

w2

0

Question 5

z1=z2

z1=z1 and z2=z

z1=−z2

none of these

Question 6

2

-1

2 or -1

None of these

Question 7

2

4

8

16

Question 8

8

17

8 or 17

None of these

Question 9

π/4

-π/4

-3 π/4

3 π/4

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x² - 2ax + b² = 0

(a²+ b²)x² - 2ax + b = 0

x² - 2ax + a² - b² = 0

2a²x² - x + a²+ b² = 0

w²