One line conditional to check if a Jetpack module is active or not.

available-modules.php

Jetpack::get_available_modules();

Array
    0    => after-the-deadline
    1    => carousel
    2    => comments
    3    => contact-form
    4    => custom-css
    5    => enhanced-distribution
    6    => gplus-authorship
    7    => gravatar-hovercards
    8    => infinite-scroll
    9    => json-api
    10   => latex
    11   => likes
    12   => markdown
    13   => minileven
    14   => monitor
    15   => notes
    16   => omnisearch
    17   => photon
    18   => post-by-email
    19   => publicize
    20   => related-posts
    21   => sharedaddy
    22   => shortcodes
    23   => shortlinks
    24   => sso
    25   => stats
    26   => subscriptions
    27   => tiled-gallery
    28   => vaultpress
    29   => videopress
    30   => widget-visibility
    31   => widgets

jetpack-module-active.php

class_exists( 'Jetpack' ) && Jetpack::is_module_active( 'carousel' )