Here the problem is to simplify the denominator (3i-4). The trick is to multiply top and bottom by 1, expressed as (-3i-4)/(-3i-4). The expression (-3i-4) is what will later be called the conjugate of (3i-4). That trick uses the general fact that

(a + ib) (a - ib) = a² - iab + iab - i² b² = a² + b²

where (a + ib) and (a - ib) are again called conjugate (as defined later). Anyway, using this trick the original expression simplifies considerably: