Imaginary numbers (beginners)

How do I solve this?

2/(3-i)

I know you rationalize the denominator, but that's where I got stuck..

please and thank you!

2/ (3-i)

first you multiply the numerator and denominator by (3+i)
u get

2 (3+i) / ( 3 - i) (3 + i) then foil the denominator and u get 9 + 3i - 3i - i^2 (negative i squared)

2 (3+i) / 10 then distribute 2 into the quantity 3 + i

and u get (6-2i) / 10

then u simply and u get 3-i / 5

To rationalize the denominator, you multiply by the complex conjugate on top and bottom. Here, the conjugate is 3+i:

(2*(3+i)) / ((3-i)*(3+i)) =

(6+2i) / (9+1) =

(6+2i) / 10 =

6/10 + 2i/10 = 3/5 + i/5.

Well i'm quite sure the variable i = the squareroot of 1

Idk how you'd solve it though. Unless you know what the variable is.