Concept:The powers of i cycle in a pattern: i1=i, i2=−1, i3=−i, i4=1, and repeat every 4 powers.This allows simplifying each entry of the given determinant before evaluating it.Explanation:First, rewrite each power of i in the matrix using the known values:i=i, i2=−1, i3=−i, i4=1, i6=(i4)(i2)=1⋅(−1)=−1, i8=(i4)2=1, i9=(i8)(i)=1⋅i=i, i12=(i4)3=1, i15=(i12)(i3)=1⋅(−i)=−i.The determinant becomes: i1i−1−11−i1−i.Now expand the determinant along the first row:=i⋅−111−i−(−1)⋅1i1−i+(−i)⋅1i−11.Compute each 2×2 determinant:−111−i=(−1)(−i)−(1)(1)=i−11i1−i=(1)(−i)−(1)(i)=−i−i=−2i1i−11=(1)(1)−(−1)(i)=1+iSubstitute back:=i(i−1)+1(−2i)+(−i)(1+i)=i2−i−2i−i−i2 (since (−i)(1+i)=−i−i2)=(i2−i2)+(−i−2i−i)=0−4i=−4i.Answer:−4i (Option D)