MTH632 Midterm Solved Subjective

MTH632 MID TERM SOLVED MCQS · (VISIT VURANK FOR MORE) · Module # 001

1. Complex Analysis related to complex numbers and their functions. We have different types of numb Integers, Rational Number i.e. , Irrational Numbers that cannot be written as

2. The decimal expression is non-terminating and non-periodic. 3. 4. Real numbers are not enough to solve our all problems if we consider an equation x2+2x+2=0 then w 5. 6. “Cardano” was first to introduce complex numbers into algebra but had misgivings abou 7. “Rafael Bombelli authored I’Algebra (1572 and 1579) a set of three books “At first , the things seeme searched until I found the proof”. 8. L.Euler (1701-1783) introduced the notation 𝑖 = −1

Module # 002

9. A complex number z can be defined as an ordered pair z=(x,y) where x,y are real numbers. 10. Complex numbers can be interpreted as points in the complex plane. 11. Real numbers is a subset of complex numbers. 12. When real numbers x are displayed as points (x,0) on the real axis the set of complex numbers inclu 13. Complex numbers of the form (0,y) corresponds to y-axis and are pure imaginary numbers when 𝑦 14. For complex number z=(x,y) the real numbers x,y are known as the real and imaginary parts of z re 15. Two complex numbers z1 and z2 are equal whenever they have the same real parts and the same im 16. The statement z1=z2 means that z1 and z2 corresponds to same point in the complex plane or z-pla 17. Let z1=(x1,y1), z2=(x2,y2) then z1=z2 iff x1=x2 and y1=y2.

Module # 003

18. Two ways to represent complex numbers are Addition of Complex numbers and Product of Complex 19. Commutative Law w.r.t Addition and Associative Law w.r.t Addition holds in Complex Numbers. 20. Addition of two complex numbers: For z1=(x1,y1), z2=(x2,y2) the addition is defined as z1+z2=(x 21. Product of two complex numbers: For z1=(x1,y1), z2=(x2,y2) the product is defined as z1.z2=(x1, 22. Any complex number z=(x,y) can be written as z=(x,y)=(x,0)+(0,y) 23. Any complex number z=(x,y) can be written as z=(x,y)=(x,0)+(0,y), Also we have (0,1)(y,0)=(0,y) so The numbers of the form (x,0) are real numbers so can simply denoted by x, numbers of the form (y number denoted by “i” then z=(x,0)+(0,1)(y,0)=x+iy 24. (0,1) is such a complex number when it is multiplied with itself then it gives -1. i.e (0,1)(0,1)=(0-1,0 25. Z=x+iy is used to represent the complex numbers and this representation is due to the mathematici

Module # 004

26. Properties of Addition of Complex Numbers: i. The addition of complex numbers follows all the properties of real numbers. ii. Additive Identity: There is a unique complex number ‘w’ such that z+w=w+z=z such numbe

27. Complex numbers can be represented by two ways. i. Ordered pair representation ii. z=x+iy form. O foundational definition on which complex number system is built while z=x+iy is used or preferred

Module # 005

28. Properties of Multiplication of Complex Numbers: i. The product of complex numbers follows all the properties of real numbers. ii. The commutative law z1z2=z2z1. The commutative implies iy=yi so z=x+iy and z=x+yi are sa The associative law z1(z2z3)=(z1z2)z3. We can write z1z2z3 without parenthesis.