Question

`(2 √(2 + 5i)) (5 √(2 - 2i))`what is the product

Answer 1

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

Step-by-step explanation:

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

`(2\sqrt[]{2}+5i)(5\sqrt[]{2}-2i)`
`=(2\sqrt[]{2}*5\sqrt[]{2})+(2\sqrt[]{2}(-2i))+(5i*5\sqrt[]{2})+(5i*(-2i))`
`=(10*2)+(-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}`