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AP EAMCET20224 Jul 2022Evening ShiftMathematicsComplex NumberActual

∑ k = 0 40 i k = x + i y ⇒ x 100 + x 99 y + x 242 y 2 + x 97 y 3 =

Options

  1. A0
  2. B- 4
  3. C4
  4. D1

Correct answer

D. 1

Step-by-step solution

Given: ∑ k = 0 40 i k = x + i y ⇒ i 0 + i + i 2 + i 3 + i 4 + i 5 + i 6 + i 7 + i 8 + . . . + i 37 + i 38 + i 39 + i 40 = x + i y ⇒ i 0 + 0 = x + i y ⇒ x + i y = 1 So, x = 1 ,   y = 0 Therefore, x 100 + x 99 y + x 242 y 2 + x 97 y 3 = 1

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