Question

Simplify: 2 + 5i / 3 - 2 i

Answer 1

2+5x4x3x2x1/3-2x1=122

Answer 2

Answer:

              $\bold{2+\frac{5i}3-2i=2-\frac{1}3i}$

or if you mean (2 + 5i)/(3 - 2i) at complex numbers

              $\bold{\dfrac{2+5i}{3-2i}=\dfrac{-4+19i}{13}=-\frac{4}{13}+1\frac{6}{13}\,i}$.

Step-by-step explanation:

$\bold{2+\frac{5i}3-2i=2+\frac{5i}3-\frac{6i}3=2-\frac{1}3i}$

But I think you mean:  (2 + 5i)/(3 - 2i) and complex numbers.

Then:

$\dfrac{2+5i}{3-2i}=\dfrac{(2+5i)(3+2i)}{(3-2i)(3+2i)}=\dfrac{6+4i+15i+10i^2}{9+6i-6i-4i^2}=\dfrac{6+19i-10}{9+4}=\dfrac{-4+19i}{13}$