Generally, a sinusoidal waveform may be represented as a complex number by using Euler's identity and freezing time at \$\small t=0\$.
Consider a sinusoid with amplitude, \$\small V_m\$ a phase angle, \$\small \phi\$, which may be written:
$$V= V_m\: e^{j(\omega t+\phi)}=V_m[cos(\omega t+\phi) +jsin(\omega t+\phi)]$$
This represents a vector of magnitude , \$\small V_m\$, that rotates as time increases from \$\small t=0\$. The real part of this complex number is the horizontal component of the vector, and the imaginary part is the vertical component of the vector
Rotating vectors are not very convenient things draw or do maths with, so instead we freeze them at \$\small t=0\$ and call them \$phasors\$. Thus, in phasor form, the above equation becomes:
$$V= V_m[cos(\phi) +jsin(\phi)]=V_me^{j\phi}$$
For example, a sinusoidal voltage signal of amplitude 3V with phase angle, \$\small \phi=0\$, would be written \$\small V= 3+j0\frac{}{}=3\$; and a sinusoidal current signal of amplitude 5A and phase angle, \$\small \phi=-30^o\$, would be represented as \$\small I=4.33-j2.5\$,
The advantage of complex notation is that we can do circuit analysis if we also express resistances and reactances in their complex forms:
$$R\rightarrow R+j0 = R$$
$$L\rightarrow 0+j\omega L = j\omega L$$
$$C\rightarrow 0+\frac{1}{j\omega C}= \frac{1}{j\omega C}= \frac{-j}{\omega C}$$
