I'm currently reading up on quantum computing and it seems like I have found some contradiction about how to represent qubits.
It is often stated that a qubit is represented as $a|0\rangle + b|1\rangle = (a, b)$ with both a and b being complex numbers.
However, it is stated just as often, that there is only one complex number needed, namely b, since to ignore the global phase shift means, that a becomes real while b stays complex. See for example: this and this.
What is it now? What don't I get here?