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MHT CET202617 April 2026Evening ShiftMathematicsComplex NumberActual

( 2 + i 2 )^7 ( 4 + i 4 )^3 =

Options

  1. A2 + i 2
  2. B( 2 + i 2 )^4
  3. C4 + i 4
  4. D( 4 + i 4 )⁻²

Correct answer

A. 2 + i 2

Step-by-step solution

Using De Moivre's theorem, ( + i )^n = n + i n . The numerator is ( 2 + i 2 )^7 = 14 + i 14 . The denominator is ( 4 + i 4 )^3 = 12 + i 12 . The given expression becomes 14 + i 14 12 + i 12 . Using the property + i + i = ( - ) + i ( - ) , we get: (14 - 12 ) + i (14 - 12 ) = 2 + i 2 . Answer: 2 + i 2

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