HELPP .. 10i/10-i solve in z=x+iy (compleks conjugate)

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HELPP .. 10i/10-i solve in z=x+iy (compleks conjugate)

Mathematics
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you can solve it by rationalizing |dw:1343807584287:dw|
i dont get it .
now multiply dominaters and nominators

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10i/10-i =(0+10i)/(10-i) =(0+10i)(10+i)/(10-i)(10+i) do the remaining few calculations and tell me the answer..
still didnt get it??
100i + 10i^2/100-i^2 ?
what should i do to get conjugate form ?
Denominator part is right but need to solve further.. \[100 - i^2 = ??\]
\[\large i^2 = -1\]
i need x+iy form.. :( confuse
Yes you will get that.. Just have patience.. Tell me : \[100 - i^2 = ??\]
The value of \(i^2 \) is -1..
i=10 ?
or 100+1 = 101 ?
Last one is right..
Similarly do it in the Numerator,,,
@greysica i^2 = -1 therefore 100 - (-1) ==?
\[100i + 10 i^2 = ??\]
100(-1)+10(-1)^2 = -100+10 =-90 ? like this ?
(100i - 10) use the fact that i^2 = -1
You can change i^2 there and not i.. remain i as such..
\[\large 100i + 10i^2 = 100i + 10(-1) = ??\]
ohh i see , 100i -10 ?
Yes...
Now you have to find this in the form z = x + iy.. So: \[\frac{-10 + 100i}{101} \implies \frac{-10}{101} + i \frac{100}{101}\]
Here I have separated both.. does it look like x + iy ??
yes , i do understand . but my teacher already give me an answer for this , he said it should be 10+i and i must find the way to get 10 + i
See your teacher said to you want to solve this by using \(10 + i\) Here we have done the same ..
The conjugate of \(10 - i\) is \(10 + i\) So we have multiplied and divide it by the conjugate that is : \(10 + i\)
i dont understand . we've got -10/101+i100/101 and my teacher said 10+i as the answer
This will not be the answer for this.. Ask him again when you will meet him..
10 + i is the conjugate for this..
I think he just said to find conjugate so then the answer should be \(10 + i\)
okay ,how about this.. 11+2i / 4+3i I do some calculation and get 2+i as the answer but my teacher said the asnwer is 2-i
Let me check..
2 - i is right..
okay i will write my calculation ..
Can you show me..??
|dw:1343814167411:dw|
|dw:1343814339078:dw|
50/25 - i (-25/25) 50/25 + i 2+i
You are doing mistake of minus.. Let me understand what you did and what the way of your teacher to solve this complex numbers problems..
|dw:1343814575597:dw|
|dw:1343814799716:dw|
Can you once try this ?? Do calculations according to it.. Try once..
ok wait
Wait..
|dw:1343815363469:dw|
|dw:1343815404009:dw|
Here x1 = 11, x2 = 4 y1 = 2 and y2 = 3
yap , the asnwer is 2+i
2 + i ??
ohh the formula from my book is wrong , omg ..
nono i mean 2-i
Is it clear to you now ??
See i show you more properly how I do this types of problems..
\[\frac{11 + 2i}{4 + 3i} \times \frac{4 - 3i}{4 - 3i} \implies \frac{44 - 33i + 8i - 6i^2}{(4)^2 - (3i)^2} \implies \frac{44 - 25i -6(-1)}{16-9i^2}\] \[\frac{44 - 25i + 6}{16 - 9(-1)} \implies \frac{50 - 25i}{16 + 9} \implies \frac{50 - 25i}{25} \implies \frac{50}{25} - i \frac{25}{25} \implies 2 - i\]
okay , thank you !! if u dont mind , i still have a little confuse , if z1/z2 = x1+iy1/x2+iy2 how about z2/2z1 ? is that means .. wait i draw
|dw:1343816101532:dw|
You have to multiply and divide by the conjugate.. Do you know how to find conjugate of a complex number ??
|dw:1343816319564:dw|
like that ?
yes well done.. Need not to multiply 2.. You can simply do this: |dw:1343816404418:dw|
hmm i see .. i really suck at this actually .. but i try to understand .. wait i try to do some calculation, thank you btw
Take your time.. Welcome dear..
|dw:1343817123248:dw| there is i^2
|dw:1343817171131:dw| and dissapear in this .. where is i^2 ?
|dw:1343817264875:dw|
\[\large -y_1y_2(i^2) = -y_1y_2(-1) \implies \color{blue}{+y_1y_2}\]
ohh I understand , so i^2 always meaning -1 in compleks form ?
Yes..
Remember: \[\large i = \sqrt{-1}\] So need to change \(i\).. \[\large i^2 = -1\] \[\large i^3 = -i\] \[\large i^4 = 1\]
|dw:1343817500482:dw| is that correct ?
hmm i see ..
Little mistake..
|dw:1343817882249:dw|