It is more common to write a qubit as

$$
|\psi\rangle = \alpha|0\rangle + \beta|1\rangle,
$$

where $\alpha, \beta \in \mathbb{C}$, i.e. to omit $i$ and get it in complex number $\alpha$.

Parameters $\alpha$ and $\beta$ are called complex amplitudes, $|\alpha|^2$ is a probability of measuring state $|0\rangle$ and $|\beta|^2$ is a probability of measuring state $|1\rangle$. So, $\alpha$ and $\beta$ (or rather square of their absolute values) can be called **"magnitude"**.

Any qubit can be rewritten as

$$
|\psi\rangle = \cos(\theta/2)|0\rangle + \mathrm{e}^{i\phi}\sin(\theta/2)|1\rangle,
$$

where $\theta$ and $\phi$ are coordinates on so-called Bloch sphere.

In this notation, $\cos^2(\theta/2)$ and $\sin^2(\theta/2)$ are probabilities (**"magnitudes"**) of measuring $|0\rangle$ and $|1\rangle$, respecitively. Parameter $\phi$ is a **phase** (or to be precise, relative phase).

You can find everything you need to understand this in this Wikipedia article: https://en.wikipedia.org/wiki/Qubit#Qubit_States

And if you need some background on complex numbers, see here: https://en.wikipedia.org/wiki/Complex_number

2

Does this answer your question? How does bra-ket notation work?. See also What is the difference between a relative phase and a global phase? In particular, what is a phase?

– glS – 2020-07-08T10:56:15.413