Uploaded April 2022 | Updated September 2026, 2 weeks ago
The invocation of the terms "real" and "imaginary" to describe complex numbers is a huge mistake in my opinion. Complex numbers are 2-dimensional numbers and nothing more. If complex numbers were taught properly, there would be no confusion. Complex numbers are 2-dimensional numbers that can only be properly and completely represented in 2x2 matrix form. Using this formulation of complex numbers, all talk of "the square root of negative 1" is also completely unnecessary. The 2x2 matrix form of complex numbers is functionally identical to the standard implementation of complex numbers, only less confusing and MORE COMPLETE. In the 2x2 matrix form of complex numbers, the "real" component occupies the forward diagonal of the matrix, and the "imaginary" component occupies the backward diagonal. All of the entries into the 2x2 matrix are real and ponderable floating point numbers. There is nothing imaginary about them. In other words, the letter "i" need NEVER appear in the matrix. If complex numbers were taught this way, we could teach them to our children. First, we would teach them how to add and multiply 1-dimensional numbers, then, we could teach them how to add and multiply 2-dimensional numbers. This is how I plan on teaching my grand kids complex numbers.
FractalWoman
The invocation of the terms "real" and "imaginary" to describe complex numbers is a huge mistake in my opinion. Complex numbers are 2-dimensional numbers and nothing more. If complex numbers were taught properly, there would be no confusion. Complex numbers are 2-dimensional numbers that can only be properly and completely represented in 2x2 matrix form. Using this formulation of complex numbers, all talk of "the square root of negative 1" is also completely unnecessary. The 2x2 matrix form of complex numbers is functionally identical to the standard implementation of complex numbers, only less confusing and MORE COMPLETE. In the 2x2 matrix form of complex numbers, the "real" component occupies the forward diagonal of the matrix, and the "imaginary" component occupies the backward diagonal. All of the entries into the 2x2 matrix are real and ponderable floating point numbers. There is nothing imaginary about them. In other words, the letter "i" need NEVER appear in the matrix. If complex numbers were taught this way, we could teach them to our children. First, we would teach them how to add and multiply 1-dimensional numbers, then, we could teach them how to add and multiply 2-dimensional numbers. This is how I plan on teaching my grand kids complex numbers.
FractalWoman
