Multiple Choice Questions on Change 1 i in modulus ndash amplitude form ........ for NDA Exam Preparation

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Multiple Choice Questions

Change 1 i in modulus ndash amplitude form ........

Mathematics (NDA) Complex Numbers
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    Change (1+i) in modulus – amplitude form? 

    √2(cos π/4 +i sin π/4) 

    Correct Answer

    √2(cos 3π/4 +i sin3π/4) 

    Incorrect Answer

    -√2(cos π/4 +i sinπ/4) 

    Incorrect Answer

    √2(cosπ/4 – i sinπ/4) 

    Incorrect Answer
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    Explanation:

     Let  (1+i) = r (cos θ +i sinθ ) , then  

    r cosθ = 1 , r sin θ=1 

    Therefore , r = √2 

    And cosθ = 1/√2 , sin θ= 1/√2 

    Thus , θ  = π/4 

    Therefore , (1+i) = √2 ( cos π/4 + i sinπ/4 ) 

     

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