KCL with phasors: how to proceed knowing effective values

[Granger]

Homework Statement

I have the following problem. Consider a circuit node where 3 sinusoidal currents with the same frequency converge, i1 i2 and i3. Knowing that the effective values of i1 and i2 are I1ef=1A and I2ef=2A. What can we say about I3ef:

Options:
$$(a)1A \leq I_{3ef} \leq 3A$$
$$(b)0 \leq I_{3ef} \leq 3A$$
$$(c)2A \leq I_{3ef} \leq 3A$$

Homework Equations

3. The Attempt at a Solution [/B]
My attempt:
So using KCL we have:
$$i_1+i_2+i_3=0$$

Using phasors
$$\overline{I_1}+\overline{I_2}+\overline{I_3}=0$$

where $$\overline{I_i}=I_ie^{j\phi_i}$$

Then
$$I_1e^{j\phi_1}+I_2e^{j\phi_2}+I_3e^{j\phi_3}=0 $$

Because $$I_i=I_{efi}\sqrt{2}$$ then:

$$I_{ef1}\sqrt{2}e^{j\phi_1}+I_{ef2}\sqrt{2}e^{j\phi_2}+I_{ef3}\sqrt{2}e^{j\phi_3}=0 $$

Now I'm stuck in this. I don't know how should I proceed from this to obtain the interval of values for I3ef. I think the complex exponentials are what is bothering me. Can someone help me?

Thanks!

 

[cnh1995]

I believe you don't need complex exponentials here. Just think about the case where you'll get maximum and minimum values for i₃.
What should be the phase difference between any two currents in that case?