Question

What is the standard form of (2-4i)(3+5i)/(3+i)?

Answer 1

expand the numerator and simplify, post what u get and then i'll tell u what to do next

Answer 2

how do u expand?

Answer 3

expand it like how you would expand a quadratic

Answer 4

like foil?

Answer 5

yes

Answer 6

ok 6-2i-20i^2/3+i

Answer 7

ok so what does i^2 evaluate to?

Answer 8

1?

Answer 9

i^2 = \[\sqrt{-1}\times \sqrt{-1}\] = -1

Answer 10

yes? so what does the numerator become now?

Answer 11

idk how would that change the numerator

Answer 12

numerator = 6-2i-20i^2
as shown above, i^2 = -1 so
6-2i-20i^2
=6-2i-20(-1)
=6-2i+20
=26-2i

do you agree?

Answer 13

yes i see how you did that

Answer 14

so now its 26-2i/3+i

Answer 15

so in math we all hate complex denominator, so we always multiply them with their conjugates to simply them

what you need to do now, is evaluate:

\[\frac{ (26-2i) }{ (3+i) }\times \frac{ (3-i) }{ (3-i) }\]

can you do that and post your answer? make sure u simplify both the numerator and the denominator

Answer 16

hold on

Answer 17

38/5-16i/5

Answer 18

so would the answer be 36-16i/5?

Answer 19

38*

Answer 20

it should be 19/2 - 4i

Answer 21

does not give that answer

Answer 22

the answer i put was correct but thanks for all the help to get me that far!!!

Answer 23

sorry my bad, that is right, 38/5 - 16i/5

Answer 24

i rechecked my working out