JSFiddle - React, Tailwind, and code Playground

HTML

<p>z = <input type="text" id="a"/> + <input type="text" id="b"/> i</p>
<p>z is <span id="contained"></span> the Mandelbrot set</p>

CSS

input {
    width: 5em;
}

JavaScript

// is a+b*i in the Mandelbrot set?
function mandelbrot(a,b) {
    var re = 0;
    var im = 0;
    var re_n = re, im_n = im;
    var trials = 0;
    for(var trials = 0; trials<100; trials++) {
        re_n = re*re-im*im + a;
        im_n = 2*re*im + b;
        re = re_n;
        im = im_n;
        if(re*re+im*im>4) {
            return false;
        }
    }
    return true;
}

function check() {
    var a = parseFloat($('#a').val());
    var b = parseFloat($('#b').val());
    if(!(isNaN(a) || isNaN(b))) {
        var contained = mandelbrot(a,b);
        $('#contained').text(contained ? 'in' : 'not in');
    } else {
        $('#contained').text('????');
    }
}

$('#a,#b').on('change keyup',check);
$('#a,#b').val(0);
check();