Answer:
[tex]30+21i\sqrt[]{2}[/tex]Explanation:
Let's go ahead and find the product as shown below;
[tex](2\sqrt[]{2}+5i)(5\sqrt[]{2}-2i)[/tex][tex]=(2\sqrt[]{2}\times5\sqrt[]{2})+(2\sqrt[]{2}(-2i))+(5i\times5\sqrt[]{2})+(5i\times(-2i))[/tex][tex]=(10\times2)+(-4i\sqrt[]{2})+(25i\sqrt[]{2})+(-10i^2)[/tex]Note that i^2 = -1, so we'll have;
[tex]=20-4i\sqrt[]{2}+25i\sqrt[]{2}-10(-1)[/tex][tex]\begin{gathered} =20-4i\sqrt[]{2}+25i\sqrt[]{2}+10 \\ =30+21i\sqrt[]{2} \end{gathered}[/tex]