The value of (1 + i)3 + (1 - i)6 is from Mathematics Complex Num

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 Multiple Choice QuestionsMultiple Choice Questions

161.

If A(z1), B(z2), C(z3) and P(z) represent complex numbers such that z1 - z = z2 - z = z3 - z, then, A, B, C lies on

  • a straight line

  • a circle

  • a parabola

  • an ellipse


162.

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


163.

If the equations ax2 + 2cx + b = 0 and ax2 + 2bx + c = 0 b  c have a common root, then the value of a + 4b + 4c will be

  • 2

  • 1

  • - 1

  • Non eof these


164.

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

  • b2 = 9ac

  • 2b2 = 9ac

  • 2b2 = ac

  • b2 = ac


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165.

The number of solutions of x2 + 3x + 2 = 0 the equation is

  • 0

  • 1

  • 2

  • 4


166.

Which of the following is correct?

  • 2 + 3i > 1 + 4i

  • 6 + 2i > 3 + 3i

  • 5 + 8i > 5 + 7i

  • None of these


167.

- 1 + - 323n + - 1 - - 323n is equal to

  • 0

  • 1

  • 2

  • 3


168.

Evaluate k = 16sin27 - icos27

  • 2i

  • - i

  • i

  • - 2i


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169.

If x2 - 4x + log1/2(a) = 0 does not have two distinct real roots, then maximum value of a is

  • - 14

  • 116

  • 14

  • None of these


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170.

The value of (1 + i)3 + (1 - i)6 is

  • i

  • 2(- 1 + 5i)

  • 1 - 5i

  • 2 + 1 - 5i


B.

2(- 1 + 5i)

1 + i3 + 1 - i6= 1 + i3 + 1 - i32= 1 +i3 + 3i1 + i + 1  - i3 - 3i1 - i2= 1 - i + 3i - 3 + 1 + i - 3i - 32= - 2 + 2i + - 2 - 2i2=  - 2 + 2i + 4 +4i2 + 8i= - 2 + 2i + 4 - 4 + 8i= 10i - 2 = 2(- 1 + 5i)


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