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

12th Standard

Reg.No. :
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Maths

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

Answer all the questions

10 x 1 = 10
1. in+in+1+in+2+in+3 is

(a)

0

(b)

1

(c)

-1

(d)

i

2. If $z=\cfrac { \left( \sqrt { 3 } +i \right) ^{ 3 }\left( 3i+4 \right) ^{ 2 } }{ \left( 8+6i \right) ^{ 2 } }$ , then |z| is equal to

(a)

0

(b)

1

(c)

2

(d)

3

3. If |z-2+i|≤2, then the greatest value of |z| is

(a)

$\sqrt { 3 } -2$

(b)

$\sqrt { 3 } +2$

(c)

$\sqrt { 5 } -2$

(d)

$\sqrt { 5 } +2$

4. z1, z2 and z3 are complex number such that z1+z2+z3=0 and |z1|=|z2|=|z3|=1 then z12+z22+z33 is

(a)

3

(b)

2

(c)

1

(d)

0

5. The principal argument of (sin 40°+i cos40°)5 is

(a)

−110°

(b)

−70°

(c)

70°

(d)

110°

6. The product of all four values of $\left( cos\cfrac { \pi }{ 3 } +isin\cfrac { \pi }{ 3 } \right) ^{ \frac { 3 }{ 4 } }$ is

(a)

-2

(b)

-1

(c)

1

(d)

2

7. The value of (1+i) (1+i2) (1+i3) (1+i4) is

(a)

2

(b)

0

(c)

1

(d)

i

8. If a=cosθ + i sinθ, then $\frac { 1+a }{ 1-a }$ =

(a)

cot $\frac { \theta }{ 2 }$

(b)

cot θ

(c)

i cot $\frac { \theta }{ 2 }$

(d)

i tan$\frac { \theta }{ 2 }$

9. If z=$\frac { 1 }{ 1-cos\theta -isin\theta }$, the Re(z) =

(a)

0

(b)

$\frac{1}{2}$

(c)

cot$\frac { \theta }{ 2 }$

(d)

$\frac{1}{2}$cot$\frac { \theta }{ 2 }$

10. $\frac { 1+e^{ -i\theta } }{ 1+{ e }^{ i\theta } }$ =

(a)

cosθ + i sinθ

(b)

cosθ - i sinθ

(c)

sinθ - i cosθ

(d)

sinθ + icosθ