PHP: show an image in php script

I want to implement this <img src="<?php echo z_taxonomy_image_url($cat->term_id); ?>" /> into the following function.

function list_my_categories($exclude = '') {
    if (!empty($exclude)) {
        $exclude = 'exclude=' . $exclude;
    }
    $categories = get_categories($exclude);
    $html = '';

    foreach ($categories as $cat) {
            if($cat->category_parent == 0) {
            <img src="<?php echo z_taxonomy_image_url($cat->term_id); ?>" />
                $html .= '<p>' . $cat->cat_name . '</p>';
                                $html .= '<p>' . $cat->category_description . '</p>';
                $childcategories =  get_categories('child_of='.$cat->cat_ID.'');
                        if(!empty($childcategories)){
                  foreach ($childcategories as $ccat) {
                  $html .= '<p>' . $ccat->cat_name . '</p>';
                              $html .= '<p>' . $ccat->category_description . '</p>';
                      }
                        }
               }
    }

    return $html;
}
add_shortcode('show-cats', 'list_my_categories');

The function shows a list of categories in WordPress, and I have another plugin which allows you to set an image for each category, so i am trying to show it…