Express A as the sum of a hermitian and skew-hermitian matrix,where
`A=[(2+3i,7),(1-i,2i)],i=sqrt-1.`

Explanation

Wehave, `A=[(2+3_(i),7),(1-i,2_(i))],i=s,"then"" "A^(theta)=(barA')=[(2-3^(i),1+i),(7,-2_(i))]`
Let `p=(1)/(2)(A+A^(theta))=(1)/(2)[(4,8+i),(8-I,0)] =[(2,4+(i)/(2)),(4-(1)/(2),0)] =p^(theta)`
thus, `p=(1)/(2)(A+A^(theta))` is a harmitian matrix.
also, let `Q=(1)/(2)(A-A^(theta))=(1)/(2)[(6i,6-i),(-6-i,4i)]`
`=[(3i,3-(1)/(2)),(-3-(1)/(2),2i)]=-[(-3i,-3+(i)/(2)),(3+(i)/(2),2i)]=-Q^(theta)`
thus `Q=(1)/(2) (A-A^(theta))` is a skew-hermitain matrix.
Now,`=[(2,4+(1)/(2)),(4-(1)/(2),0)]+[(-3i,-3-(i)/(2)),(3-(i)/(2),2i)]`
`=[(2+3i,7),(1-i,2i)]=A`
Hence, A represented as the sum of a hermaitian and a skew-hermitian matrix.