I am told by PHPStorm that I need to composer require ext-zip, however, that command is failing...

PHPStorm says

The command I am issuing is

composer require ext-zip

results in

Your requirements could not be resolved to an installable set of packages.

and

Installation failed, reverting ./composer.json to its original content.

Solution #1 - add ext-zip to your required section of composer.json:

{
    "require" : {
        "ext-zip": "*"
    }
}

Solution #2 - install php-zip extension:

Windows:

Uncomment this line in your php.ini

;extension=php_zip.dll

Linux:

sudo apt-get install php-zip

or

sudo apt-get install php7.0-zip (make sure you typed YOUR php version, you can check your version by doing php -v command)

Then, you need to restart your web server.

sudo service apache2 restart