> The need for complex numbers in describing a quantum bit. Why do we have to use complex numbers when the system is very much real? What is the real world inte

> The need for complex numbers in describing a quantum bit. Why do we have to use complex numbers when the system is very much real? What is the real world interpretation? This isn't an answer to your question but an analogy. Negative numbers probably seemed strange when you learned about them as a child. After all they don't seem to exist in the "real" world. But they're still a useful mathematical tool for turning subtraction into addition, among other things. (And negative numbers do have real-world connotations, like floor numbers below ground level.) Complex numbers are exactly like that: They are a useful tool for extending the idea of multiplication to "stuff that rotates or behaves like a wave", among other things. Don't read too much into the names; "complex" and "imaginary" are meaningless labels that simply let us keep track of how multiplication and addition differ from those operations on so-called "real" numbers. Just like "negative" numbers should not be considered "less desirable" or "more pessimistic" than positive numbers, the everyday meaning of the labels doesn't apply in a math context.