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

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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 ?
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..??
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..
Can you once try this ?? Do calculations according to it.. Try once..
ok wait
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
You have to multiply and divide by the conjugate.. Do you know how to find conjugate of a complex number ??
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 ?
\[\large -y_1y_2(i^2) = -y_1y_2(-1) \implies \color{blue}{+y_1y_2}\]
ohh I understand , so i^2 always meaning -1 in compleks form ?
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..