Question

Perform the indicated operations. Write the answer in standard form, a+bi.
(9 + 2i)(9 - 2i)

Answer 1

It can't be expressed in that form

Explanation:

From difference of two squares:

`{ \boxed{(a + b)(a - b) = ( {a}^(2) - {b}^(2) )}}`

a » 9

b » 2i

`(9 + 2i)(9 - 2i) = \{ {(9)}^(2) - {(2i)}^(2) \} \\ \\ = (81 - 4 {i}^(2) )`

but i² is -1 [ complex numbers ]

`= \{81 - 4( - 1) \} \\ = 81 + 4 \\ = 85`

Answer 2

`(9 + 2i)(9 - 2i) \: \\ this \: can \: be \: wrtten \: as \: \\ {9}^(2) - {2i}^(2) = 81 - 4 * - 1 \\ = 81 + 4 = 85 \\ then \: 85 + 0i \\ thank \: you`