Matrices of complex numbers multiplication

1. Can you put complex numbers in a matrix?
2. How do you multiply complex numbers by complex numbers?

Can you put complex numbers in a matrix?

We can represent the complex number 𝑎 + 𝑏 𝑖 as the matrix  𝑎 − 𝑏 𝑏 𝑎  . Adding and multiplying complex numbers corresponds to adding or multiplying their matrix representations. The determinant of the matrix representation of a complex number corresponds to the square of its modulus.

How do you multiply complex numbers by complex numbers?

What is Multiplication Of Complex Numbers Formula? The formula for multiplying complex numbers is: (a + ib) (c + id) = (ac - bd) + i(ad + bc).