Question

Imaginary part of third element of the second row for the Conjugate of $\left[\begin{array}{ccc}3+4i& 4& 2+5i\\ 1+2i& 2+3i& 3+5i\\ 2+7i& 9& 5\end{array}\right]$ is

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Answer 1

Matrix is $\left[\begin{array}{ccc}3+4i& 4& 2+5i\\ 1+2i& 2+3i& 3+5i\\ 2+7i& 9& 5\end{array}\right]$ Now to get the conjugate of this matrix we need to take conjugate of every element of the matrix.

Element Conjugate

3+4i 3 – 4i

4 4

2+5i 2 – 5i

1+2i 1 – 2i

2+3i 2 – 3i

3+5i 3 – 5i

2+7i 2 – 7i

9 9

5 5

So the conjugate matrix will be $\left[\begin{array}{ccc}3-4i& 4& 2-5i\\ 1-2i& 2-3i& 3-5i\\ 2-7i& 9& 5\end{array}\right]$So the third element of the second row for the matrix is 3-5i whose imaginary part is -5. So the correct answer is -5