Let n eN (that is, n is a positive whole number). The n-th root of a complex number z is z1/n. When dealing with roots we have to be careful since the n-th root function is multi-valued. In particular, there are n different possible values of w such that w" = z, all of which could properly be considered n-th roots of z! Let's explore this! ein/2. Show that eir/6, e5in/6, and e3it/2 (g) Consider the cube roots of i of i. Plot these roots on the complex plane and demonstrate graphically how ešin/6 cubes to i. [Note: Remember that multiplying by a phase e?º essentially "rotates" a point in the complex plane counterclockwise by an angle 0.] are all cube roots Find a formula for the n distinct values of the n-th root of z = rei®. As a check, test that your (h) formula implies that if w is a square root of z then so is -w.

Let n eN (that is, n is a positive whole number). The n-th root of a complex number z is z1/n. When dealing with roots we have to be careful since the n-th root function is multi-valued. In particular, there are n different possible values of w such that w" = z, all of which could properly be considered n-th roots of z! Let's explore this! ein/2. Show that eir/6, e5in/6, and e3it/2 (g) Consider the cube roots of i of i. Plot these roots on the complex plane and demonstrate graphically how ešin/6 cubes to i. [Note: Remember that multiplying by a phase e?º essentially "rotates" a point in the complex plane counterclockwise by an angle 0.] are all cube roots Find a formula for the n distinct values of the n-th root of z = rei®. As a check, test that your (h) formula implies that if w is a square root of z then so is -w.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 92E

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