#### Complex Numbers One Mark Question

12th Standard EM

Reg.No. :
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Maths

Time : 00:30:00 Hrs
Total Marks : 10
5 x 1 = 5
1. in+in+1+in+2+in+3 is

(a)

0

(b)

1

(c)

-1

(d)

i

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

(a)

1+ i

(b)

i

(c)

1

(d)

0

3. The area of the triangle formed by the complex numbers z,iz, and z+iz in the Argand’s diagram is

(a)

$\cfrac { 1 }{ 2 } \left| z \right| ^{ 2 }$

(b)

|z|2

(c)

$\cfrac { 3 }{ 2 } \left| z \right| ^{ 2 }$

(d)

2|z|2

4. The principal value of the amplitude of (1+i) is

(a)

$\frac { \pi }{ 4 }$

(b)

$\frac { \pi }{ 12 }$

(c)

$\frac { 3\pi }{ 4 }$

(d)

$\pi$

5. The least positive integer n such that $\left( \frac { 2i }{ 1+i } \right) ^{ n }$  is a positive integer is

(a)

16

(b)

8

(c)

4

(d)

2

6. 5 x 1 = 5
7. z is imaginary

8. (1)

|z1| |z2|

9. |z|

10. (2)

≤ |z1| + |z2|

11. |z1 + z2|

12. (3)

|$\bar { z }$|

13. |z1 - z2|

14. (4)

≥ |z1| + |z2|

15. |z1z2|

16. (5)

z=-$\bar { z }$