If \(\sqrt { a+ib } \)  = x + iy, then possible value of \(\sqrt { a-ib }\) is ___________

(a)

x²+y²

(b)

\(\sqrt { { x }^{ 2 }+{ y }^{ 2 } } \)

(c)

x+iy

(d)

x-iy

If z = cos\(\frac { \pi }{ 4 } \) + i sin\(\frac { \pi }{ 6 } \), then ______

(a)

|z| = 1, arg(z) =\(\frac { \pi }{ 4 } \)

(b)

|z| = 1, arg(z) = \(\frac { \pi }{ 6 } \)

(c)

|z| = \(\frac { \sqrt { 3 } }{ 2 } \), arg(z) = \(\frac { 5\pi }{ 24 } \)

(d)

|z| = \(\frac { \sqrt { 3 } }{ 2 } \), arg (z) = tan^-1\(\left( \frac { 1 }{ \sqrt { 2 } } \right) \)

.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

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

If z = 1-cos θ + i sin θ, then |z| = _____________

(a)

2 sin\(\frac { 1 }{ 3 } \)

(b)

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

(c)

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

(d)

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