iⁿ+iⁿ⁺¹+iⁿ⁺²+iⁿ⁺³ is

(a)

0

(b)

1

(c)

-1

(d)

i

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

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)

\(\sqrt { 5 } +2\)

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

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

(a)

−110°

(b)

−70°

(c)

70°

(d)

110°

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

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

(a)

2

(b)

0

(c)

1

(d)

i

If a = cos θ + i sin θ, then \(\frac { 1+a }{ 1-a } \) = ___________

(a)

cot \(\frac { \theta }{ 2 } \)

(b)

cot θ

(c)

i cot \(\frac { \theta }{ 2 } \)

(d)

i tan\(\frac { \theta }{ 2 } \)

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\(\frac { \theta }{ 2 } \)

\(\frac { 1+e^{ -i\theta } }{ 1+{ e }^{ i\theta } } \) =__________

(a)

cosθ + i sinθ

(b)

cosθ - i sinθ

(c)

sinθ - i cosθ

(d)

sinθ + icosθ