We choose the third column with two zeros, and write the determinant formula with respect to this column:
det ( A ) = + i × det [ 2 + i 3 − i 3 + i 2 + i ] = i × ( ( 2 + i ) 2 − ( 9 − i 2 ) ) = i ( 4 + 4 i − 1 − 10 ) = − 4 − 7 i {\displaystyle \det(A)=+i\times \det \left[{\begin{array}{cc}2+i&3-i\\3+i&2+i\end{array}}\right]=i\times \left((2+i)^{2}-(9-i^{2})\right)=i(4+4i-1-10)=\color {blue}-4-7i}
![{\displaystyle \det(A)=+i\times \det \left[{\begin{array}{cc}2+i&3-i\\3+i&2+i\end{array}}\right]=i\times \left((2+i)^{2}-(9-i^{2})\right)=i(4+4i-1-10)=\color {blue}-4-7i}](https://wiki.ubc.ca/api/rest_v1/media/math/render/svg/feef0ac23c6678f7c492175e53ce721b8989054a)
