Question

2-3i /
5-i
Would I multiply both by the denominator and then FOIL?

Answer 1

would you like to write this in standard form?

Answer 2

if so multiply the bottom and the top by the bottom's conjugate

Answer 3

the conjugate of a+b is a-b
the conjugate of a-b is a+b
so what is the conjugate of 5-i?

Answer 4

i+5?

Answer 5

right

Answer 6

So multiple top and bottom by i+5 and then foil?

Answer 7

(2-3i)(5+i) is the top
---------
(5-i)(5+i) is the bottom


now lets multiply

Answer 8

2*5+2i-15i-3i^2 is the top
________________
5^2-i^2 is the bottom

but what is i^2?

Answer 9

-1

Answer 10

right!

so
we have
10-13i-3(-1)
_____________
25-(-1)

10-13i+3
_________
25+1


13-13i
______
26

Answer 11

1-i
____
2

Answer 12

25i isn't 25(-1)? making -25.

Answer 13

right 25i isn't 25(-1) but
25i^2 is 25(-1)=-25
but where did you get 25i
or
25i^2

Answer 14

Oooooh, no I get what you mean now. The denominator was 25-i^2. So the final answer was/is
13-13i
------
26
which simplified to:
1-i/2
?

Answer 15

13/26-13i/26
1/2-i/2

because 26 and 13 are both divisible by 13

Answer 16

Right, so
1-i
---
2
?

Sorry if I'm beating the dead horse here.

Answer 17

Thank you so much.