1
WB JEE 2008
MCQ (Single Correct Answer)
+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$$^\circ$$
2
WB JEE 2008
MCQ (Single Correct Answer)
+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
$$\pi$$ + $$\theta$$
3
WB JEE 2008
MCQ (Single Correct Answer)
+1
-0.25

For two complex numbers z1, z2 the relation $$\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|$$ holds if

A
$$\arg ({z_1}) = \arg ({z_2})$$
B
$$\arg ({z_1}) + \arg ({z_2}) = {\pi \over 2}$$
C
$${z_1}{z_2} = 1$$
D
$$\left| {{z_1}} \right| = \left| {{z_2}} \right|$$
4
WB JEE 2008
MCQ (Single Correct Answer)
+1
-0.25

If 1, $$\omega$$, $$\omega$$2 are cube roots of unity, then $$\left| {\matrix{ 1 & {{\omega ^n}} & {{\omega ^{2n}}} \cr {{\omega ^{2n}}} & 1 & {{\omega ^n}} \cr {{\omega ^n}} & {{\omega ^{2n}}} & 1 \cr } } \right|$$ has value

A
0
B
$$\omega$$
C
$$\omega$$2
D
$$\omega$$ + $$\omega$$2
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