Question

Simplify

Answer 1

\[\frac{ 2+\sqrt{3i} }{ 5-4i }\]

Answer 2

rationalize it

Answer 3

\[\large{\frac{{(2+\sqrt{3i})}(5+4i)}{(5-4i)(5+4i)}}\]

Answer 4

can you multiply them and simplify ? @ArkGoLucky ?

Answer 5

Yeah I did that but the square root 3i is still on top and I can't rid of it

Answer 6

there are still 4 unlike terms on top so nothing simplifies

Answer 7

\[\large{\frac{(10+8i+5\sqrt{3i}+4i\sqrt{3i})}{9}}\]

Answer 8

that's enough simplification @ArkGoLucky

Answer 9

it is in the simplified form now

Answer 10

except it's 41 not 9

Answer 11

25-(4i)^2 = 25-(16(-1)) = 25+16= 41

oops sorry :P

Answer 12

but don't I need to put it into the a+bi form

Answer 13

answer given?

Answer 14

can u put that in a+b(sqrt{-1}) ? : P

Answer 15

sorry I read the problem wrong. It is much simpler. i is not under the square root. it's \[\sqrt{3}i\] thanks for your help anyways

Answer 16

medal?

Answer 17

haha okay

Answer 18

;)