# What is $j$ in the state $|\psi\rangle=\sqrt{(1-p)}|0\rangle + e^{j\phi}\sqrt{p}|1\rangle$?

What is the j in the single qubit state equation in the Quantum Phase section? https://quantum-computing.ibm.com/composer/docs/iqx/guide/introducing-qubit-phase it's not defined in the page itself (that I can see)

$$|\psi\rangle=\sqrt{(1-p)}|0\rangle + e^{j\phi}\sqrt{p}|1\rangle$$

I can see something similar referred to as i in https://en.wikipedia.org/wiki/Qubit#Bloch_sphere_representation and this other stackexchange seems to imply that they are interchangeable

When defining the state vector of a qubit in qiskit, what difference does putting "j" make?

Is "j" in this equation just the imaginary number i?

Yes, $$j$$ is just the imaginary number $$i$$.
The use of $$j$$ comes from the world of electrical engineers who use it instead of $$i$$ so there is not confusion with notation for current which is already noted $$i$$.