Complex Numbers Continued: Amplitude

This article assumes you have read our article on Polar Representation of a Complex Number Resuming from there, we had determined t = tan-1(b/a), which is called the amplitude or argument of the complex number a+ib and it is denoted by amp(a+ib). Principal amplitude: The value of t which lies in the interval (-π, π), is called the principal amplitude of the complex number a+ib. Principal amplitude of a complex number can be found as follows. First find t = tan-1|b/a| Then the principal amplitude is, a)      t, if both a and b are positive b)      π-t, if a is negative and b  is positive c)      –( π-t), if both a and b are negative d)      –t, if a is positive and b is negative Properties of amplitude: For any two complex numbers Z1 and Z2, (i)                Amp(Z1 Z2) = Amp (Z1) + Amp (Z2) (ii)              Amp(Z1 /Z2) = Amp (Z1) – Amp (Z2) We also offer English tutoring, click here for more information. SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Jamestown visit: Tutoring in Jamestown, ND.