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anonymous
 5 years ago
Find the three cube roots of the complex number 8i. Give your answers in the form x + iy
anonymous
 5 years ago
Find the three cube roots of the complex number 8i. Give your answers in the form x + iy

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2if I recall correctly, its the three spokes of a wheel; at 90degrees, 210degrees, and 330 degrees....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how do I change it into x + iy form though?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2change it into polar corrdinate form first and use Demovers thrm onit...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.28i is: z = 8(cos(90) + i sin(90)) ; now take the 1/3 power of it...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2when we take this to a normal integer power of 3 we get: z^3 = 8^3(cos(90*3) + i sin(90*3)) right? its the same for rational exponents as well.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2z^(1/3)  2(cos(90/3) + i sin(90/3))

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.290/3 = 30; the cos(30)=sqrt(3)/2 and the sin(30) = 1/2 2(sqrt(3)/2 + i 1/2) = sqrt(3) + 1i should be one of the cube roots

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2the others should be at 120 degree intervals from that one... at 150 and 270

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2(sqrt(3) + i)^2 = 2 +2sqrt(3) i (sqrt(3)+i) (2 +2sqrt(3) i) 2sqrt(3) + 6i +2i 2sqrt(3) = 8i

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.2that was cool ..... I wonder if im right on the others... 2(cos(270) + i sin(270)) 2(0 + i (1)) = 2i (2i)^2 = 4 4(2i) = 8i ..... Doh!!; well I got the first one right ;)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.22(cos(150) + i sin(150)) 2(sqrt(3)/2 + i 1/2) sqrt(3) + i; should be another one, (sqrt(3) +i)^2 = 3 1 2i sqrt(3) (2 2i sqrt(3))(sqrt(3) + i) 2sqrt(3) +2i +6i +2sqrt(3) 8i ..... well that ones good ;)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.20  (2i) is the last one;  (2i)^2 = (4i^2) = (4)(2i) = (8i) = 8i
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