Complex Numbers Test

Result

Complex Numbers Test - 6

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Weekly Quiz Competition

Question 1
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 2
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 3
1 / -0

Amp ( -1 - i) is

A
/4

B
-/4

C
-3 /4

D
3 /4
Question 4
1 / -0

If = zz', then ││equal to

A
0

B
-1

C
1

D
None of these
Question 5
1 / -0

Arg (0 + i0) is

A
0

B

C
-

D
None of these
Question 6
1 / -0

√ –8 √ –18 √ –4 is

A
24

B
24i

C
–24i

D
- 24
Question 7
1 / -0

The equation │z + 3i│²- │z + 3│² = 6 is the equation of

A
a circle

B
a straight line

C
the empty set

D
None of these
Question 8
1 / -0

Let x,y∈R,then x + iy is a non real complex number if

A
x ≠ 0

B
x ≠ 0

C
y = 0

D
y ≠ 0

Solution

If a complex number has to be a non real complex number then its imaginary part should not be zero ⇒iy≠0⇒y≠0
Question 9
1 / -0

If x = -3 + 5i, then the value of x² + 6x²+ 34x +1 is equal to

A
0

B
1

C
-1

D
none of these
Question 10
1 / -0

2√−9√−16 is equals to

A
48

B
24

C
-48

D
-24

Solution

{(22.PNG
)}
Question 11
1 / -0

(-3 + √ 27i)²+ (-3 - √ 27i)² equals

A
-2

B
-36

C
36

D
4
Question 12
1 / -0

if z = x + yi ; x, y R, then

A
z + z` = │z²│

B
zz` =│z│²

C
zz' < │z²│

D
None of these
Question 13
1 / -0

Amp(-i) is

A
/2

B
-/2

C
3 /2

D
None of these
Question 14
1 / -0

if x > 1, then a square root of 1 - √x2 - 1i is

A
√x + 1/2 + √x - 1/2 I

B
√x -1/2 + √x +1/2i

C
√x + 1/2 - √x - 1/2I

D
None of these
Question 15
1 / -0

If the cube roots of unity are 1,w,w²,then roots of the equation (x -1)³+8 = 0 is

A
-1, -1, -1

B
-1,1+2w,1+2w²

C
-1,1-2w,1-2w²

D
None of these
Question 16
1 / -0

Amp(i) is

A
/2

B
-/2

C
3 /2

D
None of these
Question 17
1 / -0

Let x,y∈R, then x + iy is a purely imaginary number if

A
x ≠ 0 , y = 0

B
x ≠ 0 , y ≠ 0

C
x = 0 , y ≠ 0

D
x = 0 , y = 0

Solution

Explanation:
Purely imaginary number is a complex number which has only imaginary part ( iy)

But if y=0 the complex number iy will become 0 which is real.

Hence the condition for a number to be purely imaginary is x=0 and y≠0
Question 18
1 / -0

If z = , then which of the following options is correct?

A
z is purely real

B
z is purely imaginary

C
Re (z) = Im (z)

D
z is any complex number