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What is the value of the determinant | array ccc i & i^2 & i^3 i^4 & i^6 & i^8 i^9 & i¹² & i¹⁵ array | where i= -1 ?

Options

  1. A0
  2. B-2
  3. C4 i
  4. D-4 i

Correct answer

D. -4 i

Step-by-step solution

| array ccc i & i^2 & i^3 i^4 & i^6 & i^8 i^9 & i¹² & i¹⁵ array |= | array ccc i & -1 & -i 1 & -1 & 1 i & 1 & -i array | aligned & =i(i-1)-1(i-(-i))-i(1+i) & =i^2-i-2 i-i-i^2=-4 i aligned

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