To divide these complex numbers you have to multiply by the conjugate of the denominator. That will look like this: [tex] \frac{5i}{4+3i}* \frac{4-3i}{4-3i} [/tex]. Multiply straight across the top and straight across the bottom to get [tex] \frac{20i-15i^2}{16-12i+12i-9i^2} [/tex]. 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: [tex] \frac{20i-15(-1)}{16-9(-1)} [/tex]. Doing the math on that we have [tex] \frac{20i+15}{25} [/tex]. We can simplify that as well as write it in standard form: [tex] \frac{15+20i}{25} [/tex]. Now we will get it into legit standard form, separating the real part of the complex number from the imaginary part. [tex] \frac{15}{25}+ \frac{20}{25}i [/tex]. That can be reduced to its final answer of [tex] \frac{3}{5}+ \frac{4}{5}i [/tex]. There you go!
