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AP EAMCET202315 May 2023Morning ShiftMathematicsComplex NumberActual

(1+i)²⁰²⁴+(1-i)²⁰²⁴=

Options

  1. A-2¹⁰¹²
  2. B2¹⁰¹³
  3. C2²⁰²⁴ i
  4. D-2¹⁰¹² i

Correct answer

B. 2¹⁰¹³

Step-by-step solution

aligned & (1+i)²⁰²⁴+(1+i)²⁰²⁴= [(1+i)^2 ]¹⁰¹²+ [(1-i)^2 ]¹⁰¹² & = [(2 i)¹⁰¹² ]+[(-2 i)]¹⁰¹² & =(2)¹⁰¹²(i)¹⁰¹²+(-2)¹⁰¹²(i)¹⁰¹² & =2 2¹⁰¹²=2¹⁰¹³ aligned

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