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

(a)

2

(b)

0

(c)

1

(d)

i

The amplitude of \(\frac{1}{i}\) is equal to _______

(a)

0

(b)

\(\frac { \pi }{ 2 } \)

(c)

-\(\frac { \pi }{ 2 } \)

(d)

\(\pi \)

The complex number z which satisfies the condition \(\left| \frac { 1+z }{ 1-z } \right| \)  = 1 lies on _________

(a)

circle x²+ y² = 1

(b)

x-axis

(c)

y-axis

(d)

the lines x+y = 1

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

(a)

cosθ + i sinθ

(b)

cosθ - i sinθ

(c)

sinθ - i cosθ

(d)

sinθ + icosθ

If ω is the cube root of unity, then the value of (1-ω) (1-ω²) (1-ω⁴) (1-ω⁸) is _________

(a)

9

(b)

-9

(c)

16

(d)

32