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Number Theory T...

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  • Question 1
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    Find the modulus and amplitude of $$-2 + 2 \sqrt 3i$$

  • Question 2
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    The inequality $$|z-4| < |z-2|$$ represents the region given by 

  • Question 3
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    Find the modulus and amplitude of $$-\sqrt 3-i$$

  • Question 4
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    (i) Every prime number is odd.
    (ii) The product of any two prime numbers is odd.
    Which of the above statements(s) is/are correct? 

  • Question 5
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    Find the value of $$x^3 + 7x^2 -x + 16$$, where $$x = 1 + 2i$$

  • Question 6
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    Consider the following statements:
    A. The sum of two prime numbers is a prime number. 
    B. The product of two prime numbers is a prime number. 
    Which of these statements is/are correct ?

  • Question 7
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    Which one of the following is the largest prime number of three digits?

  • Question 8
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    $$(1 + i)^8 + (1 -i)^8 =$$

  • Question 9
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    A student was asked to find the sum of all the prime numbers between $$10$$ and $$40.$$He found the sum as $$180.$$Which of the following statements is true?

  • Question 10
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    Find the value of: $$i^2 + i^4 + i^6$$ +..... upto $$(2n +1)$$ terms.

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