If \(\frac { z-1 }{ z+1 } \) is purely imaginary, then |z| is

(a)

\(\frac { 1 }{ 2 } \)

(b)

1

(c)

2

(d)

3

If z = x + iy is a complex number such that |z+2| = |z−2|, then the locus of z is

(a)

real axis

(b)

imaginary axis

(c)

ellipse

(d)

circle

If \(\alpha \) and \(\beta \) are the roots of x²+x+1 = 0, then \({ \alpha }^{ 2020 }+{ \beta }^{ 2020 }\) is

(a)

-2

(b)

-1

(c)

1

(d)

2

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

If \(\omega =cis\cfrac { 2\pi }{ 3 } \), then the number of distinct roots of \(\left| \begin{matrix} z+1 & \omega & { \omega }^{ 2 } \\ \omega & z+{ \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & z+\omega \end{matrix} \right| \)=0

(a)

1

(b)

2

(c)

3

(d)

4