What is the modulus of the complex number cosθ +&

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 Multiple Choice QuestionsMultiple Choice Questions

71.

The roots α and β of a quadratic equation, satisfy the relations α + β = α2 + β2 and αβ = α2β2. What is the number of such quadratic equations ?

  • 0

  • 2

  • 3

  • 4


72.

If p2, q2 and r(where p, q, r > 0) are in GP, then which of the following is/are correct ?

1) p, q and r are in GP.

2) ln(p), ln(q) and ln(r) are in AP

Select the correct answer using the code given below :

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


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73.

What is the modulus of the complex number cosθ + isinθcosθ - isinθ where, i =  - 1 ?

  • 12

  • 1

  • 32

  • 2


B.

1

 We have, cosθ + isinθcosθ - isinθ  cosθ + isinθcosθ - isinθ ×  cosθ + isinθcosθ + isinθ    By rationalization cosθ + isinθcos2θ + sin2θ cos2θ - sin2θ +2isinθcosθ    cos2θ + sin2θ = 1 cos2θ + isin2θ      cos2θ - sin2θ = cos2θ & 2sinθcosθ = sin2θSo,  cos2θ + isin2θ cos22θ + sin22θ 1


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