1
WB JEE 2011
+1
-0.25

For the real parameter t, the locus of the complex number $$z = (1 - {t^2}) + i\sqrt {1 + {t^2}}$$ in the complex plane is

A
an ellipse
B
a parabola
C
a circle
D
a hyperbola
2
WB JEE 2011
+1
-0.25

If $$x + {1 \over x} = 2\cos \theta$$, then for any integer n, $${x^n} + {1 \over {{x^n}}} =$$

A
$$2\cos n\theta$$
B
$$2\sin n\theta$$
C
$$2i\cos n\theta$$
D
$$2i\sin n\theta$$
3
WB JEE 2011
+1
-0.25

If $$\omega$$ $$\ne$$ 1 is a cube root of unity, then the sum of the series $$S = 1 + 2\omega + 3{\omega ^2} + \,\,.....\,\, + 3n{\omega ^{3n - 1}}$$ is

A
$${{3n} \over {\omega - 1}}$$
B
$$3n(\omega - 1)$$
C
$${{\omega - 1} \over {3n}}$$
D
0
4
WB JEE 2024
+1
-0.25

If $$z_1$$ and $$z_2$$ be two roots of the equation $$z^2+a z+b=0, a^2<4 b$$, then the origin, $$\mathrm{z}_1$$ and $$\mathrm{z}_2$$ form an equilateral triangle if

A
$$\mathrm{a}^2=3 \mathrm{b}^2$$
B
$$\mathrm{a^2=3 b}$$
C
$$\mathrm{b}^2=3 \mathrm{a}$$
D
$$\mathrm{b}^2=3 \mathrm{a}^2$$
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