Generate Quiz 6A1D7EE155CF2

The collection of ordered pairs (x, y) where x ∈ X and y ∈ Y is the Cartesian product of two sets X and Y, represented by X x Y. R is the set of all real numbers in this instance. Therefore, the collection of ordered pairs with a real number as the first element and another as the second is represented by R x R. The points on the Cartesian plane are represented by this set of ordered pairs.

The correct answer is ((cos θ + i sin θ)n) = (cos nθ + i sin nθ).

A foundational theorem in complex analysis, De Moivre’s Theorem establishes a relationship between the product of the powers of complex numbers in polar forms, such as angle and radius.

If a complex number in polar form is z = r(cos θ + i sin θ), where r is the radius and θ is the angle, then raising it to the power of n yields the following, according to the correct formula:

zn = rn (cos nθ + i sin nθ)

C (singleton) is the response.

a) Finite set is the set having countable elements.

b) Someone empty set is devoid of elements.

c) Singleton has only one element.

d) Infinite set had uncountable number of elements.

The set is a singleton since there is only one even prime natural number, which is 2.

The Cartesian plane is the geometric plane that a coordinate system is specified on.