Question

$(2 \sqrt{2 + 5i)} (5 \sqrt{2 - 2i)}$what is the product

Answer 1

Answer:

$30+21i\sqrt[]{2}$

Explanation:

Let's go ahead and find the product as shown below;

$(2\sqrt[]{2}+5i)(5\sqrt[]{2}-2i)$$=(2\sqrt[]{2}\times5\sqrt[]{2})+(2\sqrt[]{2}(-2i))+(5i\times5\sqrt[]{2})+(5i\times(-2i))$$=(10\times2)+(-4i\sqrt[]{2})+(25i\sqrt[]{2})+(-10i^2)$

Note that i^2 = -1, so we'll have;

$=20-4i\sqrt[]{2}+25i\sqrt[]{2}-10(-1)$$\begin{gathered} =20-4i\sqrt[]{2}+25i\sqrt[]{2}+10 \\ =30+21i\sqrt[]{2} \end{gathered}$