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anonymous
 one year ago
Find the fourth roots of the complex number " z1 = 1 + √3 * i
anonymous
 one year ago
Find the fourth roots of the complex number " z1 = 1 + √3 * i

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Part I: Write z1 in polar form. Part II: Find the modulus of the roots of z1. Part III: Find the four angles that define the fourth roots of the number z1. Part IV: What are the fourth roots of the equation " z1 = 1 + √3 * i ".

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is my answer correct? a = 1 b = sqrt(3) sqrt(a^2 + b^2) = sqrt(1 + 3) = sqrt(4) = 2 z = 2 * (1/2 + i * sqrt(3)/2) z = 2 * (cos(pi/3 + 2pi * k) + i * sin(pi/3 + 2pi * k)) z = 2 * (cos((pi/3) * (1 + 6k)) + i * sin((pi/3) * (1 + 6k))) z^(1/4) = 2^(1/4) * (cos((pi/12) * (1 + 6k)) + i * sin((pi/12) * (1 + 6k))) 2^(1/4) * (cos(pi/12) + i * sin(pi/12)) 2^(1/4) * (cos(7pi/12) + i * sin(7pi/12)) 2^(1/4) * (cos(13pi/12) + i * sin(13pi/12)) 2^(1/4) * (cos(19pi/12) + i * sin(19pi/12))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0angle is \(\frac{\pi}{3}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1you may verify the answers by rising the roots to 4th power you should get back the z1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and \[\frac{\pi}{3}\times \frac{1}{4}=\frac{\pi}{12}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Should I simplify the roots?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1i don't think you can simplify them further

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1they look good the way they are now

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1pi/12 what can you simplify here ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@satellite73 said it simplifies to pi/3?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Nope, satellite was referring to something else
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