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COMEDK2023MathematicsComplex Number

If ( 3 2 +i 3 2 )⁵⁰=3²⁵(x+i y) , where x and y are real, then the ordered pair (2 x, 2 y) is

Options

  1. A(-6,0)
  2. B(0,6)
  3. C(0,-6)
  4. D(1, 3 )

Correct answer

D. (1, 3 )

Step-by-step solution

aligned & We have, ( 3 2 +i 3 2 )⁵⁰=3²⁵(x+i y) & ( 3 )⁵⁰ ( 3 2 +i 1 2 )⁵⁰=3²⁵(x+i y) & 3²⁵ [-i (- 1 2 +i 3 2 ) ]⁵⁰=3²⁵(x+i y) & (-i)⁵⁰ ⁵⁰=x+i y & (i^4 )¹² i^2 ( ^3 )¹⁶ ^2=x+i y & (1)¹² (-1) (1)¹⁶ (- 1 2 -i 3 2 )=x+i y & 1 2 +i 3 2 =x+i y & 1+i 3 =2 x+i(2 y) & (2 x, 2 y)=(1, 3 ) aligned

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