#### 12th Standard Maths Complex Numbers English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021

12th Standard

Reg.No. :
•
•
•
•
•
•

Maths

Time : 00:10:00 Hrs
Total Marks : 10

10 x 1 = 10
1. The value of $\sum _{ i=1 }^{ 13 }{ \left( { i }^{ n }+i^{ n-1 } \right) }$ is

(a)

1+ i

(b)

i

(c)

1

(d)

0

2. If z is a non zero complex number, such that 2iz2=$\bar { z }$ then |z| is

(a)

$\cfrac { 1 }{ 2 }$

(b)

1

(c)

2

(d)

3

3. The solution of the equation |z|-z=1+2i is

(a)

$\cfrac { 3 }{ 2 } -2i$

(b)

$-\cfrac { 3 }{ 2 } +2i$

(c)

$2-\cfrac { 3 }{ 2 } i$

(d)

$2+\cfrac { 3 }{ 2 } i$

4. If (1+i)(1+2i)(1+3i)...(1+ni)=x+iy, then $2\cdot 5\cdot 10...\left( 1+{ n }^{ 2 } \right)$ is

(a)

1

(b)

i

(c)

x2+y2

(d)

1+n2

5. The value of $\left( \cfrac { 1+3\sqrt { i } }{ 1-\sqrt { 3i } } \right) ^{ 10 }$

(a)

$cis\cfrac { 2\pi }{ 3 }$

(b)

$cis\cfrac { 4\pi }{ 3 }$

(c)

$-cis\cfrac { 2\pi }{ 3 }$

(d)

$-cis\cfrac { 4\pi }{ 3 }$

6. If $\sqrt { a+ib }$ =x+iy, then possible value of $\sqrt { a-ib }$ is

(a)

x2+y2

(b)

$\sqrt { { x }^{ 2 }+{ y }^{ 2 } }$

(c)

x+iy

(d)

x-iy

7. If z=cos$\frac { \pi }{ 4 }$+i sin$\frac { \pi }{ 6 }$, then

(a)

|z| =1, arg(z) =$\frac { \pi }{ 4 }$

(b)

|z| =1, arg(z) =$\frac { \pi }{ 6 }$

(c)

|z|=$\frac { \sqrt { 3 } }{ 2 }$, arg(z)=$\frac { 5\pi }{ 24 }$

(d)

|z| =$\frac { \sqrt { 3 } }{ 2 }$, arg (z) =tan-1$\left( \frac { 1 }{ \sqrt { 2 } } \right)$

8. If x+iy =$\frac { 3+5i }{ 7-6i }$, they y =

(a)

$\frac { 9 }{ 85 }$

(b)

-$\frac { 9 }{ 85 }$

(c)

$\frac { 53 }{ 85 }$

(d)

none of these

9. If zn =$cos\frac { n\pi }{ 3 } +isin\frac { n\pi }{ 3 }$, then z1, z2 ..... z6 is

(a)

1

(b)

-1

(c)

i

(d)

-i

10. The conjugate of $\frac { 1+2i }{ 1-(1-i)^{ 2 } }$ is _______

(a)

$\frac { 1+2i }{ 1-(1-i)^{ 2 } }$

(b)

$\frac { 5 }{ 1-(1-i)^{ 2 } }$

(c)

$\frac { 1-2i }{ 1+(1+i)^{ 2 } }$

(d)

$\frac { 1+2i }{ 1+(1-i)^{ 2 } }$