Question

ASAP HELP Algebra ll

Answer 1

rationalize the denominator
\[\frac{\sqrt{-4}}{\left(7-3i\right)+\left(2+5i\right)}\]
Note: This is about the imaginary numbers.

Answer 2

what do you know about imaginary numbers ? i = what ??

1st step) first simplify the denominator (combine like terms )

Answer 3

i know about it all, i just got stuck w this example for a reason. probably because it is the 1st time to deal w such nominator.
Combine like terms we will get for the denominator
9 + 2i

Answer 4

oh okay
\[\large\rm i = \sqrt{-1}\] therefore, we can separate sqrt{-4} and write it as \[\frac{ \sqrt{-1} \cdot \sqrt{4} }{ 9+2i }\]

Answer 5

\[\sqrt{-1}\cdot \sqrt{4} =\sqrt{-4}\]

Answer 6

that's the same in the 1st place. we didn't make a progress.

Answer 7

we did....
sqrt{-4} can be wrritten as \[\sqrt{-1} \cdot \sqrt{4}\]
use the fact \[i=\sqrt{-1}\]

Answer 8

\[((i \sqrt{4)})/9 + 2i\]

Answer 9

take the square root of 4
sqrt{4} =2 \[\frac{ \sqrt{4} i }{ 9+2i} = \frac{2i}{9+2i}\]
now rationalize the denominator

Answer 10

\[\frac{ 2i }{ 9+2i } * i\]
\[\frac{ 2i^2 }{ 9i + 2i^2 }\]
\[\frac{ -2 }{ 9i -2 }\]

Answer 11

confusing...

Answer 12

hmm no that's not correct
to rationalize the denominator you should multiply the fraction by the conjugate of the denominator

Answer 13

-9i -2?

Answer 14

the conjugate of a+bi is `a-bi` change the sign of imaginary term

Answer 15

i did!

Answer 16

Now i multiply the nominator by the conjuage ?

Answer 17

\[\frac{ 2i }{ 9+2i }\]

denominator is `9+2i` what would be the conjugate ???

Answer 18

9 - 2i

Answer 19

yes that's correct.
multiply the numerator and denominator by 9-2i \[\large\rm \frac{ 2i }{ 9+2i } \cdot \frac{9-2i}{9-2i}\]

Answer 20

amazing!!. Thank youuu

The answer is \[\frac{ 18i + 4 }{ 85 }\] correct?

Answer 21

looks good

Answer 22

yw