1.

Find the value of i-12451. 12. -i3. i4. -1

Answer» Correct Answer - Option 2 : -i

Concept:

Identities:

  • i2 = -1
  • i3 = -i
  • i4 = 1
  • i4n = 1
  • i4n+1 = i
  • i4n+2 = -1
  • i4n+3 = -i

Calculation:

Let S = i-1245 = \(\rm 1\over i^{1245}\)

S = \(\rm 1\over i^{1244 +1}\)

S = \(\rm 1\over i^{4(311)+1}\)

S = \(\rm 1\over i\)

Multiply i both numerator and denominator, we get

S = \(\rm i\over i^{2}\)

S = -i



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