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Unformatted text preview: Section 1.1 Question 15: The simplest way to do this is to use polar coordinates, but I shall use the exponent laws. (The laws of exponents are part of the laws of algebra, and as such are just as valid for the complex numbers as they are for the reals or rational numbers  as long as all t he exponents are integers. If the exponents are fractional, irrational, or complex it gets a little trickier, as we shall see later on in the course). Since i^4 = 1, we see that i^{4k} = (i^4)^k = 1^k = 1, i^{4k+1} = i^{4k} i = 1 i = i, etc. Question 20: All the normal rules of algebra apply: (a) 2iz = 4, so z = 4/(2i) = 2i (b) z = (15i)(1z), so (25i)z = (15i), so z = (15i)/(25i) = (23  15i)/29 = 23/29  15i/29. (c) z(8z + (2i)) = 0, so either z = 0 or z = (2i)/8 = 1/4 + i/8. (d) z^2 = 16, so z = +4i or 4i. For the purposes of this course, "solving for z" means expressing z in one of the two standard forms (Cartesian or polar). Unless the problem asks you to simplify, however, then you may get away with an(Cartesian or polar)....
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This note was uploaded on 09/19/2011 for the course MATH 132 taught by Professor Grossman during the Spring '08 term at UCLA.
 Spring '08
 Grossman
 Algebra, Exponents

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