Problem 3: Let z1 and z2 be non-zero complex numbers. Assume that z1 and z2 have the same absolute value, i.e., |z1| = (z2| > 0. (a) Show that |z1| = |z2| if and only if there exist complex numbers w1 and w2 such that 21 = W1W2 and z2 = W1W2. (b) Explain how to choose w1 and w2 in the following special cases: (i) z2 = 21, (ii) 22 = -21, (iii) z2 is a positive real number. (c) If z1, 22 0 are given, and we have found w1 and w2 such that z1 = w1W2 and Z2 = W1w2, we can rescale them, i.e., replace wj by rwj and w2 by r- w2 for a non- zero real number r. Up to this kind of rescaling, are wj and w2 uniquely determined by z1 and zz?Z = re Given 2 , = re 19 2 W. = re want to set W,= re Z , = W , W 2 Z z = W / W 2 for ri, 12 1 , do