Question

Simplify the expression.

It is using imaginary numbers.

Answer 1

\[\frac{ 3+4i }{ 2+4i }\]

Answer 2

still need help?

Answer 3

Yep :)

Answer 4

multiply numerator and denominator by conjugate of denominator.

so bascially just do \[\frac{ 3+4i }{ 2+4i }\cdot\dfrac{2-4i}{2-4i}\]

and simplify from there

Answer 5

Okay....give me a second :)

Answer 6

for the numerator, would it be \(+~or~-~4i^2?\)

Answer 7

I think -.....

Answer 8

-, yes, but actually \(-16i^2\)

Answer 9

whoops lol I forgot to multiply the coefficients lol

Answer 10

for numerator, you should got \(6+8i-12i-16i^2\)

Answer 11

then simplify, you get it

Answer 12

yep so when you combine like terms and simplify, you get 22-4i

Answer 13

correct

Answer 14

and then the denominator simplifies to 22, correct?

Answer 15

I mean 20 lol

Answer 16

\((2+4i)(2-4i) = 4-16i^2 = 20\)

Answer 17

yeah

Answer 18

haha okay. Thank you! :)

Answer 19

no problem