Cartesian form, also known as rectangular form, is a way to represent complex numbers using their real and imaginary components. It is written in the form a + bi, where a is the real part and bi is the imaginary part.
Polar form is another way to represent complex numbers. It is written in the form r(cosθ + i sinθ), where r is the magnitude of the complex number and θ is the angle it makes with the positive real axis.
Exponential form is a way to write complex numbers using Euler's formula, which states that e^(ix) = cosx + i sinx. It is written as re^(iθ), where r is the magnitude and θ is the angle of the complex number.
Cartesian form is useful for performing arithmetic operations on complex numbers, as addition and subtraction can be done by combining real and imaginary components separately.
Polar or Exponential form is more suitable when dealing with complex numbers in polar coordinates, such as in physics or engineering problems involving polar coordinates. It is also useful for visualizing and understanding the geometric properties of complex numbers.