Complex Analysis - Maths KU

48 Chapter 1 Complex Numbers and the Complex Plane
i 2
y
i 5
i
i 3
Figure 1.29 Figure for Problem 50
i 4
x
Figure 1.29. Use this mnemonic to find i n for the following values of n:
5, 9, 13, 17, 21, ... ; i n =
6, 10, 14, 18, 22, ... ; i n =
7, 11, 15, 19, 23, ... ; i n =
8, 12, 16, 20, 24, ... ; i n =
(b) Reinspect the powers n in the four rows in part (a) and then divide each
these powers by 4. Based on your discovery, discern an easy rule for determining
i n for any positive integer n. Use your rule to compute
i 33 = ,i 68 = ,i 87 = ,i 102 = ,i 624 = .