For a complex number x + iy, if x > 0 and y < 0 then the number lies in the.
When x > 0 & y < 0, the quadrant contains positive Xaxis and negative Yaxis
Therefore, the point lies in the fourth quadrant.
If U = set of all whole numbers less than 12, A = set of all whole numbers less than 10, B = Set of all odd natural numbers less than 10, then what is (A∩B)’?
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {1, 3, 5, 7, 9}
A ∩ B = {1, 3, 5, 7, 9}
(A ∩ B)’ = U  (A ∩ B)
(A ∩ B)’ = {0, 2, 4, 6, 8, 10, 11}
If z_{1} = 4, z_{2} = 4, then z_{1} + z_{2} + 3 + 4i is less than
Which of the following is a finite set?
If P and Q are two sets such that n(P) = 120, n(Q) = 50 and n(P ∪ Q) = 140 then, n(P ∩ Q) is:
n(P)=120
n(P∪Q)=140
n(Q)=50
n(P∪Q)=n(P)+n(Q)−n(P∩Q)
140 = 120 + 50  n(P∩Q)
n(P∩Q) = 30
A point z = P(x,y) lies on the negative direction of y axis, so amp(z) =
P(x,y) lies on the 3rd or 4th quadrant
So, according to the question, points lies in 3rd quadrant
i.e. 3(π/2)
The argument of the complex number i
z = i
Comlex number z is of the form x + iy
x = 0, y = 1
arg(z) = π − tan−1y/x
⇒ π − tan−11/0
= π  (π/2)
⇒ π  π/2
⇒ π/2
The modulas of the complex number 1 + √3i is
√(1)^{2} + (√3)^{2}
= 2
The argument of the complex number 1 – √3
z = a + ib
a = 1, b = √3
(1, √3) lies in third quadrant.
Arg(z) = π + tan^{1}(b/a)
=  π + tan^{1}(√3)
=  π + tan^{1}(tan π/3)
=  π + π/3
= 2π/3
The amplitude of a complex number is called the principal value amplitude if it lies between.
x = z cos θ and y = z sin θ satisfies infinite values of θ and for any infinite values of θ is the value of Arg z. Thus, for any unique value of θ that lies in the interval  π < θ ≤ π and satisfies the above equations x = z cos θ and y = z sin θ is known as the principal value of Arg z or Amp z and it is denoted as arg z or amp z.
We know that, cos (2nπ + θ) = cos θ and sin (2nπ + θ) = sin θ (where n = 0, ±1, ±2, ±3, .............), then we get,
Amp z = 2nπ + amp z where  π < amp z ≤ π
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