The resulting value on expansion of [tex](3+\sqrt{-16} )(6-\sqrt{-64} )[/tex] is 50
Given the surd product;
[tex](3+\sqrt{-16} )(6-\sqrt{-64} )[/tex]
Since the square root of a negative number will give a complex number that is:
[tex]\sqrt{-1} = i[/tex]
The given expression above then becomes:
[tex](3+4i )(6-8i)[/tex]
Expand
[tex]=(3+4i )(6-8i)\\=18-24i+24i-32i^2\\=18-32i^2\\=18-32(-1)\\=18+32\\= 50[/tex]
Hence the resulting value on expansion is 50.
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