Complex Numbers Test

Result

Complex Numbers Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

If Z = 3√/2+i/2, Z³ then equals

A
i

B
1

C
-1

D
- i
Question 2
1 / -0

If (1 + i) (1 + 2i) (1 + 3i) …… (1 + n i) = x + y i; where x, y ∈ R and n ∈ N, then 2X5X10X…..X (1 + n²) =

A
√x² + y²

B
x² - y²

C
x² + y²

D
√x² - y²
Question 3
1 / -0

If ω is a cube root of unity, then the value of (1 + ω)(1 + ω²)(1 + ω⁴)(1 + ω⁸) ...... up to 2n factors is

A
1

B
-1

C
2

D
None of these
Question 4
1 / -0

Distance of the representative of the number 1 +i from the origin ( in Argand’s diagram ) is

A
2

B
1

C
√2

D
none of these

Solution

Let P(x,y) represent the complex number Z=x+iy in the complex plane(Argand plane) and let O(0,0) be the origin

Then we have OP=√x2+y2

Here Z=1+i so that P(x,y)=P(1,1)

Hence OP=√1+1=√2
Question 5
1 / -0

If |z−2|=|z−6| then locus of z is given by :

A
a circle

B
a straight line parallel to x axis

C
a straight line parallel to y axis

D
none of these
Question 6
1 / -0

The complex number z is such that │z│ = 1, z ≠ - 1 and w = (z - 1)/(z + 1). The real part of w is

A
│z - 1│²/│z + 1│²

B
- 1

C
√ 3/│z│²

D
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Re-Attempt Weekly Quiz Competition

Complex Numbers Test - 2

Result

Complex Numbers Test - 2

Score

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Rank

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SHARING IS CARING

Question 1

i

1

-1

- i

Question 2

√x2 + y2

x2 - y2

x2 + y2

√x2 - y2

Question 3

1

-1

2

None of these

Question 4

2

1

√2

none of these

Solution

Question 5

a circle

a straight line parallel to x axis

a straight line parallel to y axis

none of these

Question 6

│z - 1│2/│z + 1│2

- 1

√ 3/│z│2

0

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√x² + y²

x² - y²

x² + y²

√x² - y²

│z - 1│²/│z + 1│²

√ 3/│z│²