Quadratic Equation of Complex Number (Part - 4) - Complex Numbers and Quadratic Equations, Math Video Lecture - Class 11 | Best Video for Class 11

hello friends this video on complex
number part 4 is brought to you by exam
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watching this video please make sure
that you have washed complex number part
1 part 2 part 3 understand quadratic
equation quadratic equation is X square
plus V expressed in video the maximum
power is 2 with real coefficients a B
and C and E is not equal to 0 because a
is 0 this will become 0 but we want the
mini important to be X square here the
solution is X going to minus B plus
minus root b square minus 4ac y2 so
sometimes this becomes negative so we
get iPhone but remember it's very simple
minus B plus minus D by 2 and D is going
to be square minus 4ac it's awesome push
in here X square plus 3 is equal to 0 X
square is equal to minus 3 or X is 2
root of minus 3 so when I say root of
minus 3 is equal to root of minus 1 into
root of 3 and root of minus 1 is going
to I into root 3 so X is equal to I and
this is a complex number because this is
a imaginary part so let's take for
example x squared plus X plus 1 is below
0 this is the of the form X square DX
plus C is equal to 0 here a is equal to
1 B is equal to 1 C is not one the
solution we know is d is get 2 minus V
plus minus root D Square minus 4 AC by
we have learned as formula in the early
levels so minus V is equal to minus 1
because V is going to 1 plus minus v
square is going to 1 squared minus 4a is
equal to 1 C is 10 to 1 by 2 into H that
Sigma so this becomes minus 1 plus minus
root 1 minus 4 square 2 minus 3 by 2 so
root of minus 3 is equal to UC minus 1
plus minus root of minus 1 into 2 12 3
by the root of minus 1 is going to light
the
becomes one plus minus root three why so
we can also say is equal to minus 2
minus 1 by 2 plus minus root 3 by 2 and
this is the answer
they are two complex number actually and
say you take this here this is two
complex number 1 by 2 plus root 3 by 2 I
by easier missing sorry or minus 1 by 2
minus root 3 by 2 I so these are the
answer for the equation because we are
talking about minus root 1 so minus root
1 is 5
let's solve one more problem here the
problem says we have a number complex
number in this form and I want to when
all the value of theta where this is
purely real so that means the I Part A
plus IB this is B 0 will be 0 this will
become 0 for the second come on so our
goal here is to convert this into a plus
I B form spreads to this XI plus 2 I
sine theta by 1 minus 2i sine theta
let's rationalize this 1 plus 2i sine
theta and here 1 plus 2i sine theta by
dividing and multiplying them 1 plus 2 I
sine theta
snare but you gated 1 square plus 2 sine
theta square and let's multiply this 3
into 1 is 3 plus 6i sine theta plus y
sin theta into 1 is 2 I sine theta plus
y into 2 y is going to 4i square I
square sine square theta I square Delta
minus 1 so this will become 3 minus 4
sine square theta plus I into a sine
theta by 1 plus 4 sine square theta and
also one loves for sine square theta now
we want to make this real so this part
should be equal to 0 so we say a
sine theta by 1 plus 4 sine square theta
should be equal to 0 so that means sine
theta should be equal to 0 so theta
should be n pi where n is obviously any
real number sorry any integer because if
you see a real number thing is not its
meaning integers 1 2 3 effects is like
that that is our answer let's take one
more problem so if X plus I by
inspecting this we have to prove that X
square plus y square is 1 to 1 so we see
that if we can find X minus iy here and
then we can just multiply X plus I Y
into X minus iy we get X plus X square
plus y square to get X minus iy we have
to convert this into T plus PI Q form so
let's create that form takes plus I by E
+ IV into e minus IV it's rationalize
this is IV by E + IV
spot you get is a plus I B whole square
it is the e square minus v square plus
TB I and here you get a square plus B
square correct so if you solve this this
become a square minus minus v square by
a square plus B square plus I into 2 ABY
a square plus B square so this is of the
form P plus Q I so now similarly X minus
iy if you want to try you can just say X
minus iy is equal to a square minus B
Square by a square plus B Square minus I
into 2 AV by a square plus B square now
you have X plus iy we have X minus 7
will multiply X plus iy into
X minus iy is equal to we'll multiply
this two so we'll get what a square
minus v square plus 2 a VI into a square
minus v square minus vbi a and this is a
square plus v square come whole square
and this side is equal to x square plus
y square now I have to solve this so
this is nothing but you see this this is
X this is y this is X by X plus y into X
minus y so you get x squared plus y
squared Hui plus Omega 1 square minus y
square so my this is square plus v
square come whole square correct you
could have also said like this to
simplify the problem instead of saying
this we know that a square minus B
Square minus 2 ABI is nothing but a
minus B sorry a t Plus this is plus here
this a plus VI iike post pair and this
guy is a minus B Aika pulse Phi because
a minus b whole square is equal to a
square minus B Square minus 2 a B a and
a plus B a whole squares will do a
square minus B square plus 2 ETA and
this is the one now we can say X square
plus y square is equal to now you see
this is nothing but a plus bi into a
minus B a the hole is I am saying
possible I am taking taking out a square
common and now this I am saying a square
plus B Square now a plus bi into a minus
B a is a square plus B square whole
square is there this is their most part
my a square plus B
square whole square this is more square
here so what you get is a square plus B
square whole square by a square will be
square nose was the new one and this you
saw what I've done
I have personalize this you get X plus I
by 1 then we form X minus iy for X minus
I Y multiplied this 2 to go to X plus y
square and I solve this and I well I'm
solving this I found that the item on
the right hand side became one thank you
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