If A(z₁), B(z₂), C(z₃) and P(z) represent complex numbers such that $\left|{\mathrm{z}}_1 - \mathrm{z}\right| = \left|{\mathrm{z}}_2 - \mathrm{z}\right| = \left|{\mathrm{z}}_3 - \mathrm{z}\right|$, then, A, B, C lies on

• a straight line

• a circle

• a parabola

• an ellipse

If the complex numbers z, z, and origin form vertices of an equilateral triangle, then the value of z₁² + z₂² will be

• z₁z₂

• z₁ + z₂

• 2z₁z₂

• z₁ - z₂

If the equations ax² + 2cx + b = 0 and ax² + 2bx + c = 0 $\left(\mathrm{b} \ne \mathrm{c}\right)$ have a common root, then the value of a + 4b + 4c will be

• 2

• 1

• - 1

• Non eof these

If one root of ax² + bx + c = 0 is twice the other root, then

• b² = 9ac

• 2b² = 9ac

• 2b² = ac

• b² = ac

165.

The number of solutions of ${\mathrm{x}}^2 + 3\left|\mathrm{x}\right| + 2 = 0$ the equation is

• 0

• 1

• 2

• 4

Which of the following is correct?

• 2 + 3i > 1 + 4i

• 6 + 2i > 3 + 3i

• 5 + 8i > 5 + 7i

• None of these

${\left[\frac{- 1 + \sqrt{\left(- 3\right)}}{2}\right]}^{3\mathrm{n}} + {\left[\frac{- 1 - \sqrt{\left(- 3\right)}}{2}\right]}^{3\mathrm{n}}$ is equal to

• 0

• 1

• 2

• 3

$\mathrm{Evaluate} \sum _{\mathrm{k} = 1}^6\left(\sin \left(\frac{2\mathrm{k\pi }}{7}\right) - \mathrm{icos}\left(\frac{2\mathrm{k\pi }}{7}\right)\right)$

• 2i

• - i

• i

• - 2i

If x² - 4x + log_1/2(a) = 0 does not have two distinct real roots, then maximum value of a is

• $- \frac{1}{4}$

• $\frac{1}{16}$

• $\frac{1}{4}$

• None of these

The value of (1 + i)³ + (1 - i)⁶ is

• i

• 2(- 1 + 5i)

• 1 - 5i

• 2 + 1 - 5i