Using objects with vectors

A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i² = −1.

A complex number can be represented as a vector in the complex plane, where the real part corresponds to the x-coordinate and the imaginary part to the y-coordinate. This allows us to visualize and perform vector operations like addition and subtraction on complex numbers.

In C++, a vector of complex numbers can be created using std::vector and std::complex. The std::complex template class is part of the <complex> header and represents complex numbers with a specified underlying floating-point type (e.g., double, float).

The right shift operator in C++ is written as >> and is used to shift the bits of a number to the right by a specified number of positions. It’s a bitwise operator, meaning it works directly on the binary representation of numbers.

In C++, an iterator is like a smart pointer that allows you to traverse through elements in a container (like vector, list, map, etc.) without knowing the underlying structure. It’s part of the Standard Template Library (STL) and is essential for working with algorithms and containers in a generic way.

In C++, std::complex<double> is a class template specialization from the <complex> header that represents a complex number with both real and imaginary parts stored as double precision floating-point values.

semantics: the meaning of words, phrases or systems

In the code snippet prev(points.end(), 2)->real(), here's what each part means:

points.end(): This returns an iterator pointing to the element after the last element in the vector points.

prev(points.end(), 2): The prev function takes an iterator and a number of positions to move back. In this case, it moves back 2 positions from the end of the vector, effectively pointing to the second-to-last element.

->real(): This accesses the real part of the complex number at the iterator's current position.

So, prev(points.end(), 2)->real() gets the real part of the second-to-last complex number in the points vector.

Objects are instances of classes. For example, a complex number object contains data members like the real and imaginary parts. You access these members using the dot operator (.), like complexNumber.real().

Iterators are special objects that act like pointers to elements within a container (like a vector). They allow you to traverse the container. When using iterators, you access the members of the object they point to using the arrow operator (->), like iterator->real().

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