Question

Consider the equation z^11 = (-1 + i). Find the value of z which satisfies this equation and which has the second smallest positive argument theta, 0 < theta < 2pi. Express your answer as z = re^{itheta} where r = and theta = When entering your answers, use "pi" as needed, and for roots use a^(1/n) for the nth root of the number a (e.g. 2^(1/5) is how we enter the 5th root of 2.)

Name: Consider the equation z^11 = (-1 + i). Find the value of z which satisfies this equation and which has the second smallest positive argument theta, 0 < theta < 2pi. Express your answer as z = re^itheta where r = and theta = When entering your answers, use "pi" as needed, and for roots use a^(1/n) for the nth root of the number a (e.g. 2^(1/5) is how we enter the 5th root of 2.)
Uploaded: 2020-10-02T05:32:20-08:00
Duration: 2 min 15 s
Channel: Uma Kumari
Description: Consider the equation z^11 = (-1 + i). Find the value of z which satisfies this equation and which has the second smallest positive argument theta, 0 < theta < 2pi. Express your answer as z = re^itheta where r = and theta = When entering your answers, use "pi" as needed, and for roots use a^(1/n) for the nth root of the number a (e.g. 2^(1/5) is how we enter the 5th root of 2.)

          Consider the equation z^11 = (-1 + i). Find the value of z which satisfies this equation and which has the second smallest positive argument theta, 0 < theta < 2pi. Express your answer as z = re^{itheta} where r = and theta = When entering your answers, use "pi" as needed, and for roots use a^(1/n) for the nth root of the number a (e.g. 2^(1/5) is how we enter the 5th root of 2.)

Consider the equation z^11 = (-1 + i). Find the value of z which satisfies this equation and which has the second smallest positive argument theta, 0 < theta < 2pi. Express your answer as z = re^itheta where r = and theta = When entering your answers, use "pi" as needed, and for roots use a^(1/n) for the nth root of the number a (e.g. 2^(1/5) is how we enter the 5th root of 2.)

Added by Diane J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Uma Kumari

10/02/2020

Step 1

To do this, we find the magnitude and argument of the complex number. The magnitude is given by: $r = \sqrt{(-1)^2 + (1)^2} = \sqrt{2}$ The argument is given by: $\theta = \arctan{\frac{1}{-1}} = \arctan{-1} = -\frac{\pi}{4}$ Since we want the positive Show more…

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Consider the equation z^11 = (-1 + i). Find the value of z which satisfies this equation and which has the second smallest positive argument theta, 0 < theta < 2pi. Express your answer as z = re^(itheta), where r = and theta =. When entering your answers use "pi" as needed, and for roots use a^(1/n) for the nth root of the number a (e.g. 2^(1/5) is how we enter the 5th root of 2).