00:00So in this video we will discuss nine questions of complex number and these play
00:04Those who solve it, subscribe to the location and that too in one and a half years.
00:08This is the matrix, if we see this location then this is that Veli, this is it and we
00:16a k into a value is completed so k which is a one so a one reading number
00:29When you come here, that is, today the fisher par-chisht gas
00:59When i is divided by 2, it becomes 3i, that is, 2 plus 3 will come today, this element is the remaining two.
01:06If it is in 9 option then it is in two 9 option cut left part and left option
01:12element except this one we're looking at here divided by 2i it becomes
01:18divided by 2i to 6
01:293 means 2 minus 2 minus 3i because minus 3i then later option number will become a
01:40Now the answer to this is in front of us as we move forward.
01:45The next question is now let's call it so it's simply this long iota to the power n plus iota
01:56K pyawar n plus bun and n's valley two to 11 going from so then after
02:01If I put valley then the first thing that comes out is iota to the power of 2 plus iota.
02:07Four plus one is what I end up with, iota to the power of 11 plus iota to the power of 2.
02:17MRETER a sequence show that it is iota
02:27So let's subscribe to this bar and now we know that if power conjunctivity is
02:45like the Fiery Four
02:47So you are thirty five you are five you will do what you want
02:52Let's assume that power 3 is in these four lo in root place core 001 what is this
02:59half will go
03:01Ayot's
03:02iota q plus iota power 4 value of iota power 4 value of 1 square minus 1 value of iota
03:09i
03:09And the value of iota cube minus i is 1, that is, it cancels out and becomes 4 consecutive zeros.
03:15So then this is also 0 and this 7 plus 10 is also 0, so we have 2 iota left.
03:20power 10
03:21power of 2 iota 11 plus iota is required plus power of iota value minus 12 iota is required
03:281
03:28What is the value of 12 to the power of iota i.e. 4 to the power of iota into 3 iota to the power of 4
03:341
03:34That means what will be created by multiplying 1 disaster 3 times?
03:38This means that 1-1 will cancel out and 2 iota to the power of 11.
03:42The value of 8 to the power of iota will be 1
03:451 into 1 into
03:47iota cube key value
03:48iota scree key value
03:50Manas 1 into iota
03:51Means Manas Iota
03:53That means 2 iota of manus will go
03:55The final answer to this is
03:57Now in the next Gyochan I simply
03:59The executive wants to keep
04:00iota to the power 1000
04:02No 1000 left inside
04:05The Power of Iota
04:06If I bought 1000 mangoes then what was left inside
04:09The Power of Iota
04:101 plus 2 plus 3 plus 4
04:12We just proved its value.
04:15is 0 then later
04:16The value of this equation becomes 0
04:18Now here it is in front of us
04:20How many ana of the next equation
04:22is non-zero integral
04:24The solution to this equation is
04:26Then later on I'll be here
04:28The symbol of modulus is given in both the sites.
04:30That is, the symbol of modulus
04:32What is modulus and root inside
04:33a square plus b square means
04:35under root 1 plus 2 minus 2
04:38square 4 means
04:40under root 1 plus 4 5
04:42Now root is 5
04:43We can write root 5 as
04:455 to the power 1 by 2
04:47Now this barwala x this one will come
04:49power of 5 1 by 2 x is equal to 5
04:51x means
04:53what happened 1 by 2 x is equal to x
04:55x is x equal to 1
04:58which ever
04:59It doesn't mean it is true
05:01This equation has no solution, that is, any solution
05:03This equation does not have
05:05then later in the next
05:06has given us that
05:08what is the principle argument of
05:10minus 1 minus iota
05:12Then later we know that the equation of this also
05:15There is a standard form
05:16not a complex number equation
05:18The standard form of a complex number is
05:21a plus iota too
05:22Now the argument here is
05:24That the argument of this complex number also
05:26z is equal to theta
05:29which is the x-axis
05:30forms an angle with the leaves
05:32That is theta
05:34argument z or theta is equal to 10
05:36inverse y upon x
05:39what happens to y
05:40This is b and x.
05:42Because if we look at the graph
05:44plot then imaginary part
05:46real part on the y axis
05:48x axis i.e. imaginary part
05:50upon real part imaginary part
05:52what is b minus 1
05:54what is real part b minus 1
05:56minus 1 upon minus 1
05:58That means it got cancelled and became
06:00That is, the value of 10 theta
06:02If it is 1 then at how many angles
06:041 comes with a value of 45
06:06So the value of theta in Fivad is
06:0845 Dig Di Agar
06:09Dig di me anse kare to and
06:11If we do it in radians, then 5 by 4
06:16In Fivad
06:17In Fivad
06:17next question is
06:19I have given so much
06:19if z is equal to x plus
06:21y so in Fivad
06:25what does it represent
06:26This equation is in Fivad
06:28We know what a conjugate is.
06:30If a plus iota b complex
06:32If the number is then it will be conjugated
06:34a minus iota b here
06:36x plus iota y is so it's conjugate
06:38x minus iota y
06:40x plus iota y into x minus iota y
06:43a plus b into a minus b
06:44If we establish our identity then it will be created.
06:46a squared minus b squared
06:48That is, x is square minus iota y
06:50iota x square y is square
06:52The value of iota x squared
06:54minus 1 into minus
06:56what will become plus
06:57x squared plus y squared
07:00plus z
07:02what will become modulus modulus of
07:04under root x square plus y square
07:07We know the modulus of
07:08This formula is direct
07:10under the square root of
07:12under root will be removed
07:14x squared plus y squared
07:16plus 4 into
07:18x plus iota y
07:20plus x minus iota y
07:23plus iota y's answer
07:24Know that 2x
07:264 into 2x minus 48
07:28is equal to 0
07:292x is square plus 2y is square
07:31plus 8x is equal to 48
07:342 will be given on this side
07:36will divide
07:36So in our footer next
07:37x square plus y square plus 4x is equal to 24
07:41Now we know that
07:43This is the equation
07:45This cycle will now be known in detail.
07:47Which equation remains how?
07:48for example x plus y is equal to something then it would be
07:53straight line
07:54equation
07:56This cycle is like this
07:58equation again in the matter now
08:00The next question is this
08:03that how many values
08:05that iota of
08:06power minus 2n
08:07that n can be any integer
08:11So now we talk about one thing
08:12put the value of n as 0
08:14So on putting the value of n as 0
08:16power of any number
08:18What does it become when you put 0?
08:201 So then one thing is
08:22iota of one then
08:24Its value came to 1
08:26Now we will put 1 thing in one
08:28So what will come 1 upon
08:30I iota comes to this i.e. 1 upon
08:32in minus 1
08:34So 1 upon minus 1
08:35open multiplied by minus 1
08:37So it becomes minus 1.
08:39So one value is its ban
08:40one minus 1 now why is that no value or disc
08:43Because it is not odd on aa
08:45so iota minus
08:47The value iota minus iota cannot occur
08:50because you minus 2n
08:52So whatever its power may be
08:53It will always be some even number.
08:56Can be of integer type
08:58But there will never be an odd number.
08:59Not an odd number
09:01Like minus 1 minus 3
09:03Minus 5 is not of this type
09:05And it is being created only on the value of those types
09:07this iota or else
09:09minus iota then again in the bar
09:11It has 2 possible values
09:131 minus 1 will give the answer
09:15final 2 now
09:17The next question is this one
09:20Here we are
09:21delayed in question
09:22z is equal to 1 plus iota
09:24iota is equal to under root minus 1
09:27And we are asked for its modulus
09:29So at most we will simplify from A
09:31The value of z is put as 1 plus iota
09:33plus 2 upon
09:351 plus iota now we know
09:37If the denominator is also complex
09:39If it is a number then simplify it.
09:41to conjugate with
09:42numerator and denominator i.e.
09:45Upan will multiply it
09:46So what is the conjugate of 1 plus iota?
09:49multiply it by 1 minus iota
09:51so that A square minus B square
09:53from the identity of
09:54Get a real number
09:56This will come to our notice and remove the imaginary number.
09:58from the denominator so what will it become
10:011 is square minus iota is square
10:03The value of iota is squared
10:04minus 1 minus 1 into minus plus
10:07That means 1 plus 1
10:08minus 2 in the numerator
10:102 minus 2
10:13iota 1 plus iota
10:14plus now 2
10:16So what does this 1 plus 1 become?
10:182
10:19I accepted 2 of these
10:20So 1 minus iota
10:22The 2 above this bottom 2
10:24cancel so what next for us
10:251 plus iota plus 1 minus iota
10:28plus iota to minus iota cancel
10:301 plus 1 ≠ 2 so its final answer is next
10:332 Now in this question it is kept in
10:36that this complex number 1 minus iota
10:38under root 3 upon 1 plus iota
10:40What is the argument for under root 3?
10:43That means we have been asked theta
10:45So even more than this
10:46We will simplify it like the one above.
10:48into its conjugate numerator and denominator
10:51multiplied it
10:52So what will be its conjugate?
10:531 plus iota under root 3 in the denominator
10:56So its conjugate is
10:581 minus iota under root 3
11:00went up and down
11:02It became low
11:041 plus 3
11:06who is that
11:07a is dry minus b is dry
11:091 minus iota is dry
11:12The root of 3 is 3
11:13iota is dry
11:15minus 1 into minus plus
11:171 plus 3
11:191 minus iota in the numerator
11:22under root of 3
11:24The hole is dry
11:26So 1 minus
11:283 iota is dry
11:29That means minus 1 has arrived.
11:311 minus 3
11:32minus 2 iota under root 3
11:341 minus 3 minus 2 iota under root 3
11:37upon 4
11:391 plus 3 4
11:40Now from here we
11:43are called separate
11:44real part to imaginary part
11:46So it became
12:11any
12:12of complex numbers
12:13argument
12:17minus root of 3 upon 2
12:19upon in the minus of 1 by 2
12:20From this 2 it is cancelled
12:21minus to minus cancel
12:23That means 10 theta is equal to root 3
12:25which theta is equal to 60
12:27on degree if in degree then
12:29and in radians
12:31pi by 3
12:32If the value is root 3 then the value of this argument will come
12:3460 degrees or pi by 3
12:36radian
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