Unformatted text preview: ior or senior year once you’ve completed the Calculus sequence. It is in that course that the
true power of the complex numbers is released. But for now, in order to fully prepare you for life
immediately after College Algebra, we will say that functions like f (x) = x21 have a domain of all
real numbers, even though we know x2 + 1 = 0 has two complex solutions, namely x = ±i. Because
x2 + 1 > 0 for all real numbers x, the fraction x21 is never undeﬁned in the real variable setting.
+1 9 With the exception of the exercises on the next page, of course. 3.4 Complex Zeros and the Fundamental Theorem of Algebra 3.4.1 227 Exercises 1. We know i2 = −1 which means i3 = i2 · i = (−1) · i = −i and i4 = i2 · i2 = (−1)(−1) = 1.
Use this information to simplify the following.
(a) i5 (b) i304 (c) (2i)3 (d) (−i)23 2. Let z = 3 + 4i and w = 2 − i. Compute the following and express your answer in a + bi form.
(a) z + w
(b) w − z w
(f) w3 (c) z · w
w 3. Simplify the followin...
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