The quaternion number system extends the complex numbers. It's the quotient of two directed lines in a three-dimensional space, or, equivalently, as the quotient of two vectors. Quaternions are generally represented in the form

a + bi + cj + d k

where a, b, c, and d are real numbers; and i, j, and k are the basic quaternions.

• Write a class that defines a quaternion and operations with it.

Details

• Define a class Quaternion that will store 4 coefficients of quaternion
  • The default constructor must accept four double-typed parameters.
• Overload an equality operation for your class to compare two quaternion objects.
  • Compare corresponding coefficients of the quaternion objects, and return true if they are equal; otherwise return false.
  • The operator must accept constant reference to the Quaternion object.
• Overload an addition operation for your class to add two quaternion objects.
  • The operator must accept constant reference to the Quaternion object.
  • Add corresponding coefficients of the quaternion objects and return result.
    • The operator must return the Quaternion object. Do not modify current object.
• Overload a subtraction operation for your class to subtract two quaternion objects.
  • The operator must accept constant reference to the Quaternion object.
  • Subtract corresponding coefficients of the quaternion objects.
    • The operator must return the Quaternion object. Do not modify current object.
• Overload a multiplication operation for your class to multiply the quaternion object by a scalar number.
  • Multiply all coefficients of the quaternion object by the double-typed value
    • The operator must return the Quaternion object. Do not modify current object.
• All operators must be const members
• Make sure that your program compiles without errors

please write in C++ for my OOP class