Thesedays I am trying to understand the role and working of complex numbers. Previously, I posted my question here but I could not get the required answer. Rightnow I am reading about a complex numbers in Toronto University's website and there I read a very confusing and irritating statment which as follows: The strength of an electromagnetic field. This is a directly measurable quantity that is measured by a complex number. That number will be purely real if the field is all electric with no magnetic component, purely imaginary if the field is all magnetic with no electric component, and in other cases will have a non-zero real part and a non-zero imaginary part. So according to this statement in the absence of electric field we have an imaginary magnetic component. So, what is meant by an imaginary magnetic component? Let's consider a laboratory where we have an Electromagnetic field. Now let's remove the electrical component from field so that only magnetic component remains. So, will this magnetic component have no effect on compass? Secondly, if it has the effect on the compass (since I believe it should be the case). Then, the magnetic field should have the strength which is measured or represented by imaginary number (according to the scientists). So, how an imaginary number can give the answer (the real valued answer)?