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MHT CET202313 May 2023Morning ShiftMathematicsComplex NumberActual

The value of i ²⁴⁸+ i ²⁴⁶+ i ²⁴⁴+ i ²⁴²+ i ²⁴⁰ i ²⁴⁹+ i ²⁴⁷+ i ²⁴⁵+ i ²⁴³+ i ²⁴¹ , ( i = -1 ) is

Options

  1. Ai
  2. B1
  3. C-1
  4. D- i

Correct answer

D. - i

Step-by-step solution

aligned & i²⁴⁵+i²⁴⁶+i²⁴⁴+i²⁴²+i²⁴⁰ i²⁴³+i²⁴⁷+i²⁴⁵+i²⁴³+i²⁴¹ & = i²⁴⁰ (i^8+i^6+i^4+i^2+1 ) i²⁴¹ (i^8+i^6+i^4+i^2+1 ) & = i²⁰⁰ i²⁴¹ & = 1 i & = i i^2 =-i aligned

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