Question

can anybody please help me with this?

Answer 1

Do I first substitute (1-i sqrt of 2) in x?

Answer 2

mhmm

Answer 3

yes, just subsitute

Answer 4

and how do I simplify next?

Answer 5

multiply by conjugate of denominator both , denominator and numerator so that you multiply by one which doesn't change the value of expression but helps you to simplify

Answer 6

to multiply with \[2 + (1+i \sqrt {2})\]

Answer 7

?

Answer 8

first simplify it a little:
denominator : 2-(1-isqrt2) = 1+isqr2 its conjugate: 1- isqrt2
but your conjugate could be correct as well

Answer 9

plug it in and resolve the top. then mult top and bottom by the conjugate of the bottom to get your answer

Answer 10

what ans you get?

Answer 11

I am sorry... I am confused!!! :(

Answer 12

ok ,
after substitution:
\[\frac{ (1-i \sqrt 2)^2 }{ 2-(1-i \sqrt 2) }=\frac{ 1 -2i \sqrt 2 + i^2*2 }{1+i \sqrt 2 }=\frac{ 1-2 i \sqrt 2-2 }{1+i \sqrt 2}\]
remember i^2 =-1

Answer 13

now multiply that by:
\[\frac{ 1- i \sqrt 2 }{ 1- i \sqrt 2 }\]

Answer 14

\[\frac{ 1 -2i \sqrt{2} -2 +1 - i \sqrt {2} }{ 1^{2} - (i \sqrt{2})^{2} }\]

Answer 15

is this correct?

Answer 16

denominator is good but numerator is
\[(1- 2 i \sqrt 2 -2)(1-i \sqrt 2)= (-1-2 i \sqrt 2)(1-i \sqrt 2)=-(1+2 i \sqrt 2)(1-i \sqrt 2)\]

Answer 17

thanks!!!

Answer 18

what is your answer ?

Answer 19

i still didnt finish :(

Answer 20

I dont know how to continue!!

Answer 21

ok
\[-(1+2 i \sqrt 2)(1- i \sqrt 2)=-(1-i \sqrt 2 + 2 i \sqrt 2 - i^2*2*\sqrt 2^2)\]

Answer 22

= \[-5- i \sqrt 2\]

Answer 23

this is for the numerator

Answer 24

yes

Answer 25

and for denominator?

Answer 26

how do I simplify it

Answer 27

1- (-2)=3

Answer 28

thank you so much!!!!!!

Answer 29

yw