Divide the following complex numbers (5i)/(4+3i)

To divide these complex numbers you have to multiply by the conjugate of the denominator.  That will look like this:  .  Multiply straight across the top and straight across the bottom to get  .  In the denominator, the 12i and -12i cancel each other out, which is nice.  Now, in both the numerator and the denominator we have an i-squared.  i-squared is equal to -1, so we will make that substitution in our solution:  .  Doing the math on that we have  .  We can simplify that as well as write it in standard form:  .  Now we will get it into legit standard form, separating the real part of the complex number from the imaginary part.  .  That can be reduced to its final answer of  .  There you go!