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What is the value of the determinant  where ?

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  1. 0
  2. -2
  3. 4i
  4. -4i

Answer (Detailed Solution Below)

Option 4 : -4i
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Detailed Solution

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Concept:

i2 = -1 , i3 = - i, i4 = 1, i6 = - 1 , i8 = 1 , i9 = i, i 12 = 1, and i15 = - i

 

Calculations: 

Given determinant is 

Since, we have, 

i2 = -1 , i3 = - i, i4 = 1, i6 = - 1 , i8 = 1 , i9 = i, i 12 = 1, and i15 = - i

=

=i(i - 1) + 1(-i - i) - i (1 + i)

= i2 - i - 2i - i - i2

= - 4i

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