Question

Rationalize the denominator of square root of negative 16 over open parentheses 1 plus i close parentheses plus open parentheses 6 plus 3 i.

quantity of negative 16 plus 28 i over 33
quantity of 16 plus 28 i over 65
quantity of negative 12 plus 28 i over 40
quantity of 12 plus 28 i over 58

Answer 1

@jhonyy9

Answer 2

can you rewrite it using numbers ?

Answer 3

so i will try it too

Answer 4

\[\frac{ \sqrt{-16}}{ (1+i)+(6+3i) }\]

Answer 5

so you have wrote it right sure ?

Answer 6

so do you know what mean rationaliz the denominator ?

Answer 7

that is the square root of -16 as the numerator

Answer 8

And the denominator is correct

Answer 9

The reciprocal is created by inverting the numerator and denominator of the starting expression. Since we now have a radical in the denominator, we must rationalize this denominator. Multiply top and bottom by the conjugate of the denominator

Answer 10

Thats from an example on google.

Answer 11

no - for example :

sqrt 3
--------------- =
(3-2i) +(1-i )

so rationaliz the denominator mean that you need to do anything for eliminate the terms with ,,i" from denominator - yes ?

in this case multiplie numerator and denominator by conjugate of denominator

do you know it how and what mean conjugate ?

Answer 12

yes

Answer 13

so than try it so

Answer 14

idk how

Answer 15

you have said that you know what mean conjugate - yes ?

Answer 16

i had the incorrect definition

Answer 17

so suppose there is in denominator (a+ib) + (c+id)
- and because you know formula (a+b)(a-b)=a^2 -b^2
- and you know again that i^2 = -1

- so try using these what i have wrote above

ok ?

Answer 18

ok

Answer 19

than what will be the conjugate of denominator in case of your exercise ?

Answer 20

so there are (1+i)+(6+3i)
(a + b)

- let being so
- and you know formula (a+b)(a-b)=a^2 -b^2

us this please

Answer 21

so you need multiplie the numerator and the denominator by (a-b)

yes ?

Answer 22

so what will be (a-b) in this case of your exercise ?

Answer 23

so than you know a=(1+i) and b=(6+3i)
- so a-b ho will be ?

Answer 24

how - sorry

Answer 25

do you understand it ?

Answer 26

so the conjugate will be (1+i)-(6+3i)
yes ?

Answer 27

multiplie by this the numerator and denominator - ok. ?

Answer 28

((1+i)+(6+3i))*((1+i)-(6+3i)) = (1+i)^2 -(6+3i)^2

do you like continue it ? but dont forget it that this is just the denominator and you need again multiplie by conjugate of denominator the numerator too

Answer 29

@princesssleelee are you here please ?

Answer 30

im here

Answer 31

First simplify getting: