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Manipal MET2018MathematicsComplex Number

If ( 3 -i)⁵⁰=2⁴⁸(x-i y) , then x^2+y^2 is equal to

Options

  1. A2
  2. B4
  3. C8
  4. D16

Correct answer

D. 16

Step-by-step solution

( 3 -i)=2 ( 6 -i 6 ) aligned ( 3 -i)⁵⁰ & =2⁵⁰ ( 6 -i 6 )⁵⁰ & =2⁵⁰ ( 3 -i 3 ) & =2⁵⁰ ( 1 2 -i 3 2 ) aligned But ( 3 -i)⁵⁰=2⁴⁸(x-i y) aligned & & x & =2 and y=2 3 & & x^2+y^2 & =4+12=16 aligned

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