Complex Analysis Lec 1 by Maqsood Ali Abbas

For BS & MS classes

🔶Abdul Hanan (1016)
🔶 Morning
👉Q#1
An ordered pair (x, y) is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.

It helps to locate a point on the Cartesian plane.

The numeric values in an ordered pair can be integers or fractions.

The order is important because a point named by the ordered pair ( 5, 3 ) is not at the same location as the point named by the ordered pair ( 3, 5 ).

👉Q#2
The symbol for the set of complex numbers is 'C'.

👉Q#3
Pi (π), which begins with 3.14, is one of the most common irrational numbers.

👉Q#4
The value of "r" is always positive because r is the distance between the positions. As distance is always Positive so r is positive.

👉Q#5
After multiplying a complex number Z by scalar k there will be no effect on amplitude but it effect its modulus.

[AbdulRehman-eqwc]

Abd-ul-rehman (2216)
Q1:what is an ordered pair?
Ans: ordered pair is a composition of the x-coordinate (abscissa) and the y-coordinate (ordinate) having two values written in a fixed order within paratheses
Properties:
(1) (x, y) and (y, x) are different
(2) (x, y)=(y, x) if x=y
(3) (x, y)=(a, b) if a=x and b=y
Q2: what is symbol for set of complex number?
Ans:symbol is C
Q3:
Ans: irrational number is √2
Q4:
Ans:r is positive because distance is always positive
Q5:
Ans:Multiply a complex number by scalar there will bi no affect at amplitude but it effect it's modulus

[mathsearchers]

Mehwish Naseer 2231

Q:1...Two pairs written in a certain order is called ordered pair & it's usually written in parentheses (x, y)
Q:2....The symbol is used for complex number is usually "C"
Q:3...."Pi" is an irrational number like "e" which has value 3.14...
Q:4.... "r" is the distance and distance always measure in positive form
Jis constant sy multiply kry gy may b wo utna hi increse ho jye ga

[dawoodsilvester]

Dawood Silvester 2236 evening
Q:What is formula of complex numbe?
Ans: z=x+iy
Where i symbol operation of addition and muplication of complex number
Whera complex is denoted with C
X=real number y=imaginary number

[nimramustafa]

Nimra Mustafa 2206
Complex num denoted by C.
√3 is an irrational.
Because distance always positive.

[mishalch]

Mafia Zafar(1049)Morning
Q#1(Ans).Each point in the plane can beidentified by a pair Of number of the pair measure a horizental distance and called the abscissa, or first coordinate or x-coordinate.
Q#2(Ans).The set of complex numbers extends the set of visualized in the complex plane.
Set of complex number represented by the Latin capital letter "C".
Q#3(Ans).Pai is the irrational number.Value is 3.141592.

[arooshamubeen]

Aroosha Mubeen (2225) evening
Q:1-An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.
Q:2- The symbol used for complex number is "C".
Q:3- π is probably the most famous irrational number, π=3.14...
Q:4- (r) is a distance and distance is always positive.
Q:5- Modulus will change but amplitude remains same.

[faizaanwar]

Q:1.What is an ordered pair?
Ans:A pair of element a, b having the property that (a, b) =(u, v) if and only if
a=u, b=v.
Q:2.What is the symbol for complex number?
Ans:The symbol for complex number is Z=X + iY.
Q:3.Give example of an irrational number?
Ans: Pi =
Q:4.Why the value of r is always positive in polar form?
Ans:Because r is a distance.It cannot be negative.It's the variation of theta that moves you in different quadrants, not r.

[ishfaqahmad-rudr]

Aleeza Ishfaq 1003 morning 5th semester
Q#1:An ordered pair consists of two elements that are written in the fixed order. So, we define an ordered pair as: 
. The pair of elements that occur in particular order and are enclosed in brackets are called a set of ordered pairs. 
. If ‘a’ and ‘b’ are two elements, then the ordered pair is (a, b).
. In an ordered pair (a, b), a is called the first component and b is called the second component.
Q#2:the symbol of complex numbers is "C".
Q#3:irrational number :
Golden ratio φ :1.618033988749....
Q#4: r is always positive because r is the modulus(always positive) of the complex numbers.
Q#5:by the scalar multiple of complex numbers modulus will be changed but amplitude will remain same.

[knowledgeofmathematicsonli]

Muhammad Arslan 2246
Q1(Ans)An order pair is two numbers for which the order in which they are given is important.
Q2(Ans)symbol 'C' is used for denoted complex numbers.
Q3(Ans) √3, 2√2, &π are also complex numbers.
Q4(Ans)'r' represent the distance and distance can never be negative so 'r' (distance) is always positive.
Q5(Ans) when we multiply a scalar number by complex number then it's modulus change but it's amplitude remain same.

[nidaasghar]

Nida Asghar (935810)
Ans1: An order pair is a composition of the X coordinate and Y coordinate, having two values written in a fixed order with parentheses Order pairs are also called 2-Tuples or sequences of length 2.
Ans2: The standard symbol for the set of complex number is "C".
Ans3: pi (22/7), is one of most common example of irrational numbers.
Ans4: r is the distance b/w the positions, distance always positive so, r will be positive.
Ans5: A scalar multiple only effects on the modulus, but amplitude remains the same.

[rimshazahid]

Rimsha Zahid 2204 (evening)
Q1. What is an ordered pair?
Ans. An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parantheses.
The numeric values in an ordered pair can be integers or fractions.
Q2. What is the symbol for set of complex number?
Ans. The set of complex number is represented by the Latin capital letter " C".
Q3. Example of irrational number?
Ans. Pi is a irrational number.
We cannot write down a simple fraction that equals Pi.
The popular approximation of 22/7 = 3.1416

[anayasubhan]

Insha Akhtar (1009)
Q:1 An ordered pair is a composition of x and y coordinate having values written in a fixed order in parenthesis like (x, y).
Q:2 Symbol of set of complex number is'C'.
Q:3 22/7 is an example of irrational number.
Q:4 Modulus values can never be negative.
Q:5 change in modulus but no change in amplitude..

[syedabukhari]

Q.1 we represent Complex numbers with C
Q.2 orderd pair refers to set of two numbers used to locate a point in co-ordinate plane.
Example: (2, 3) is an ordered pair.
(2, 3) and (3, 2) both are different to each other.
Q.3 pie is an irrational number and its value is 3.14....
Q.4 r is always positive because r is modulus and modulus is always +ve.
Q.5 modulus will change but amplitude remains same .
Arooj bukhari 1007 Morning

[taimourakhtar]

Question #1 what is order pair?
Ans An ordered pair is a composition of the x coordinate (abscissa) and the your coordinate (ordinate), having two values written in a fixed order within parentheses. 
Denoted by (x, y)
Question#2 What is abbreviation for Complex Numbers?
Ans we denote complex numbers by "C"
Z=a+bi where a is real number and other is Imaginary
Question#3
Ans: π (pi) is another example of famous irrational Numbers
Question#4
Ans: r is positive because r is modulus and modulus is always positive.
Question#5
Ans Modulus will change but Amplitude remains same.
Taimour Akhtar 1012 morning

[jabirkhan]

Nosheen bibi 2255 (evening)
Q 1.What is an orderd pair?
Ans. An orderd pair is a composition of the x coardinate (abscissa)and the Y coardinate(ordinate)having tow values written in a fixed order within paratheses the numaric values in an orderd pair can be integers of fractions
Q2.what is the symbol for the set of complex number?
Ans. The set of complex number is represented by the Latin capital letter "C".
Q3.Example of irrantional number?
Ans.Pi is airrational number
We cannot write down a simple fractions that equals Pi.
The popular approximation of 22/7=3.1416

[qandyqueen]

Q1:An ordered pair is a composition of x coordinate(abscissa)and y coordinate (ordinate)having two values written in a fixed order .It is also called 2 tuples.Ordered pair=(x, y).
X=abscissa, the distance measure of a point from primary axis x and y=ordinate, the distance measure of a point from secondary axis Y'.
Q2:C is a symbol of complex number and{a+bi:a, b€R, i=square root -1}.
Q3:e, Eulers no is an irrational number and e=2.71828.
Q4:r represents the absolute value or modulus .In polar form r represents the distance and distance always positve and modulus also positive thats why r is positive.
Q5: It effects only modulus and does not any change on amplitude or argument.

[masoomshah]

Q;1)Ordered pair is set of two numbur which comes out from the multiplication of two sets are in the form of (x, y) used to Reffer the point in a plane.
*belong to real num
*x=abssica, y=ordinate
Q:2)symbol of complex numbers is C.
Q:3) We have a irrational numbur named Pii.
Q;4) because r is the modulus value which is always +.
Q;5) If we multiply the complex numbur it doesn't effect amplitude.

[rjumair]

Sahar Nadeem 2226
1-An order pair is a composition of x coordinate and y coordinate having two values written in a fixed order in parentheses
2-Symbol of complex number is C.
3-Example of irrational number π.
4-Because r is length which is always positive.
5-Change in mod but no change in amplitude.

[fiazahmad]

Fiaz Ahmad 2218

What are complex Numbers ??

any Number which contain _iota_

xi+y