Question 377230
We can decompose the fraction into (-2)/3i - 5i/3i = -5/3 - (2/3)i. However, even though this method works for this problem, this is not the standard way of rewriting a complex number.

The standard way to simplify a complex number in the form (a+bi)/(c+di)is to multiply top and bottom by the complex conjugate of c+di, or c-di. This becomes

={{{(a+bi)(c-di)/(c+di)(c-di)}}}
={{{((ac+bd)+(bc-ad)i)/(c^2 + d^2)}}}