are they in direct current?
No. A real valued phasor is still a phasor with a phase of zero. The time dependence has been 'hidden' but one must always keep in mind that the phasor value is the amplitude and phase of a sinusoidal function of time.
If, in fact, the frequency of the sinusoid were zero, all capacitors would be have infinite impedance and all inductors would have zero impedance.
The fact that this isn't the case in the circuit given means that the actual voltages and currents are sinusoids of non-zero frequency.
This circuit is easily solved by superposition which allows the solution to be written by inspection.
For example, the (phasor) voltage across the current source is, by superposition:
$$1V \cdot \frac{j1}{j1 + (-j1)||1} + 2A \cdot j1||(-j1)||1 \Omega $$
The first term is with the current source off and is an application of voltage division.
The second term is with the voltage source off and is just the current multiplied by the equivalent impedance seen by the source.
Since the frequency and/or capacitance and inductance values are not given, one cannot convert the phasor solutions to time dependent functions. One might as well consider the (angular) frequency to be \$\omega = 1\$ and the capacitance and inductance to be \$C = 1F\$ and \$L = 1H\$ respectively.
For a different frequency, the values of the capacitance and inductance would scale appropriately such that impedances are unchanged.
If you want the equation from what the English-speaking world calls Kirchoff's Voltage Law (KVL), for the right-side mesh of your circuit, it's
$$-V_{C3} + V_{R2} + V_{C2} + V_{Zn} + V_{L3} = 0$$
You will now have to guess (or work out) what direction convention I chose for each element, since you didn't include any polarity markers in your schematic.
Then you will have to substitute in the characteristic behavior of each element for the voltage variables, to get an equation that just depends on the mesh currents.
From there (and the similar equation for the left side mesh) you will be able to solve for the currents.
Best Answer
You can't determine it. It has to be given or assumed.