Pre-Calc Exam Notes 145

Pre-Calc Exam Notes 145 - Complex Numbers • Section 6.3...

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Unformatted text preview: Complex Numbers • Section 6.3 145 x y − i radicallow 3 2 + i 2 − radicallow 3 2 + i 2 | z |= 1 120 ◦ 120 ◦ 120 ◦ Figure 6.3.3 Notice from Example 6.13 that the three cube roots of i are equally spaced points along the unit circle | z | = 1 in the complex plane, as shown in Figure 6.3.3. We see that consec- utive cube roots are 120 ◦ apart. In general, the n n th roots of a complex number z will be equally spaced points along the circle of radius | z | 1/ n in the complex plane, with consecutive roots separated by 360 ◦ n . In higher mathematics the Fundamental Theorem of Alge- bra states that every polynomial of degree n with complex coefficients has n complex roots (some of which may repeat). In particular, every real number a has n n th roots (being the roots of z n − a ). For example, the square roots of 1 are ± 1, and the square roots of − 1 are ± i . Exercises For Exercises 1-16, calculate the given expression....
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.

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