Question

Simplify:
2 + 5i / 3 - 2 i

Answer 1

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

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

`\bold{(2+5i)/(3-2i)=(-4+19i)/(13)=-(4)/(13)+1(6)/(13)\,i}`.

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:

`(2+5i)/(3-2i)=((2+5i)(3+2i))/((3-2i)(3+2i))=(6+4i+15i+10i^2)/(9+6i-6i-4i^2)=(6+19i-10)/(9+4)=(-4+19i)/(13)`