Question

Simplify
(6 + 3i)(6 − 3i)

Answer 1

`\displaystyle 45`

Explanation:

`\displaystyle (6 + 3i)(6 - 3i) = 36 - 9i^2 = 36 - 9[-1] = 36 + 9 = 45`

Extended Information on the Complex Number System

`\displaystyle √(-1) = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = 4\:[Any\:multiple\:of\:four]`

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Answer 2

45

Explanation:

(6 + 3i)(6 − 3i) =6 (6 − 3i)+ 3i(6 − 3i)

= 36 -18i +18i-9
`i^(2)`

if
`i^(2) =-1`

36 -18i +18i-9
`i^(2)` = 36-9(-1)

=36+9

=45

=36-9i^2

=6^2 - (3i)^2