# How do you perform the operation and write the result in standard form given (sqrt14+sqrt10i)(sqrt14-sqrt10i)?

Mar 15, 2018

It is well known that the product yields the difference of two squares.

#### Explanation:

$\left(\sqrt{14} + \sqrt{10} i\right) \left(\sqrt{14} - \sqrt{10} i\right) = {\left(\sqrt{14}\right)}^{2} - {\left(\sqrt{10} i\right)}^{2}$

The square is the inverse of the square root, therefore, only the argument remains:

$\left(\sqrt{14} + \sqrt{10} i\right) \left(\sqrt{14} - \sqrt{10} i\right) = 14 - 10 {i}^{2}$

Substitute ${i}^{2} = - 1$:

$\left(\sqrt{14} + \sqrt{10} i\right) \left(\sqrt{14} - \sqrt{10} i\right) = 14 - 10 \left(- 1\right)$

Multiplication by -1 changes the sign:

$\left(\sqrt{14} + \sqrt{10} i\right) \left(\sqrt{14} - \sqrt{10} i\right) = 14 + 10$

$\left(\sqrt{14} + \sqrt{10} i\right) \left(\sqrt{14} - \sqrt{10} i\right) = 24$