iⁿ+iⁿ⁺¹+iⁿ⁺²+iⁿ⁺³ is

(a)

0

(b)

1

(c)

-1

(d)

i

 The value of \(\sum_{n=1}^{13}\left(i^{n}+i^{n-1}\right)\) is

(a)

1+ i

(b)

i

(c)

1

(d)

0

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

.If a = 3+i and z = 2-3i, then the points on the Argand diagram representing az, 3az and - az are _________

(a)

Vertices of a right angled triangle

(b)

Vertices of an equilateral triangle

(c)

Vertices of an isosceles

(d)

Collinear

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

z is imaginary

(1)

z = -\(\bar { z } \)

|z|

(2)

≤ |z₁| + |z₂|

|z₁ + z₂|

(3)

≥ |z₁| + |z₂|

|z₁ - z₂|

(4)

|\(\bar { z } \)|

|z₁z₂|

(5)

|z₁| |z₂|