1
WB JEE 2008
+1
-0.25

The value of $${(1 - \omega + {\omega ^2})^5} + {(1 + \omega - {\omega ^2})^5}$$, where $$\omega$$ and $$\omega$$2 are the complex cube roots of unity is

A
0
B
32 $$\omega$$
C
$$-$$32
D
32
2
WB JEE 2008
+1
-0.25

Let $$\alpha$$, $$\beta$$ be the roots of $${x^2} - 2x\cos \phi + 1 = 0$$, then the equation whose roots are $${\alpha ^n},{\beta ^n}$$ is

A
$${x^2} - 2x\cos n\phi - 1 = 0$$
B
$${x^2} - 2x\cos n\phi + 1 = 0$$
C
$${x^2} - 2x\sin n\phi + 1 = 0$$
D
$${x^2} + 2x\sin n\phi - 1 = 0$$
3
WB JEE 2008
+1
-0.25

The principal amplitude of $${(\sin 40^\circ + i\cos 40^\circ )^5}$$ is

A
70$$^\circ$$
B
$$-$$ 110$$^\circ$$
C
110$$^\circ$$
D
$$-$$ 70$$^\circ$$
4
WB JEE 2008
+1
-0.25

A and B are two points on the Argand plane such that the segment AB is bisected at the point (0, 0). If the point A, which is in the third quadrant has principal amplitude $$\theta$$, then the principal amplitude of the point B is

A
$$-$$ $$\theta$$
B
$$\pi$$ $$-$$ $$\theta$$
C
$$\theta$$ $$-$$ $$\pi$$
D
$$\pi$$ + $$\theta$$
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