If n is positive integer, then (1 + i)n + (1 - i)n is equal

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171.

If n is positive integer, then (1 + i)n + (1 - i)n is equal to

  • 2n - 2cos4

  • 2n - 2sin4

  • 2n + 2cos4

  • 2n + 2sin4


C.

2n + 2cos4

1 + in + 1 - inUsing polar form,1 + i = 2cosπ4 + isinπ4and 1 - i = 2cosπ4 - isinπ4Now, 1 + in + 1 - in= 2cosπ4 + isinπ4n + 2cosπ4 - isinπ4n= 2ncos4 + isin4 + 2ncos4 - isin4= 22ncos4= 2n + 2cos4


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172.

The square root of 2i is

  • 1 + i

  • 1 - i

  • 2i

  • - 2


173.

The root ofthe equation 2x - log10(x) = 7 is between

  • 3 and 3.5

  • 2 and 3

  • 3.5 nad 4

  • None of these


174.

The roots of the quadratic equation 2x2 + 3x + 1 = 0 are

  • rational

  • irrational

  • imaginary

  • None of these


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175.

Roots of equation x3 - 6x + 1 = 0 lie in the interval

  • (2, 3)

  • (3, 4)

  • (3, 5)

  • (4, 6)


176.

If 3 - i22 + i = A + iB where A and B are real numbers, then A and Bare equal to

  • A = - 4, B = 2

  • A = 2, B = - 4

  • A = 2, B = 4

  • None of these


177.

If 1, w and w2 are the cube roots of unity, then the value of (1 - w + w2)(1 + w - w2) is equal to

  • 4

  • 0

  • 2

  • 3


178.

The sum of the real solutions of equation 2x2 + 51 = 1 + 20x is

  • 5

  • 24

  • 0

  • None of these


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179.

The quadratic equation whose roots are 13 + 2 and 13 - 2, will be

  • 7x2 - 6x + 1 = 0

  • 6x2 - 7x + 1 = 0

  • x2 - 6x + 7 = 0

  • x2 - 7x + 6 = 0


180.

If z = ilog2 - 3, then the value of cos(Z) will be

  • i

  • 2i

  • 1

  • 2


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