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Use De Moivres theorem to change the given complex number to the fo.pdf

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Use De Moivre\'s theorem to change the given complex number to the form a + bi, where a and b are real numbers. (- Squareroot 3/2 - 1/2 i)^4 Solution ( -sqrt3/2 -i/2)^4 Polar form = r*e^i*theta r = sqrt[ (-sqrt3/2)^2 + (1/2)^2 )] = 1 theta = tan^-1(-1/2 /-sqrt3/2) = pi +pi/3 = 4pi/3 ( -sqrt3/2 -i/2)^4 = (re^i*theta)^4 = r^4e^i*4theta = 1*e^i*16pi/3 = cos16pi/3 + isin16pi/3 = -0.5 -i*0.866.

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Use De Moivre's theorem to change the given complex number to the form a + bi, where a and b are real numbers. (- Squareroot 3/2 - 1/2 i)^4 Solution ( -sqrt3/2 -i/2)^4 Polar form = r*e^i*theta r = sqrt[ (-sqrt3/2)^2 + (1/2)^2 )] = 1 theta = tan^-1(-1/2 /-sqrt3/2) = pi +pi/3 = 4pi/3 ( -sqrt3/2 -i/2)^4 = (re^i*theta)^4 = r^4e^i*4theta = 1*e^i*16pi/3 = cos16pi/3 + isin16pi/3 = -0.5 -i*0.866

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Use De Moivres theorem to change the given complex number to the fo.pdf

  • 1. Use De Moivre's theorem to change the given complex number to the form a + bi, where a and b are real numbers. (- Squareroot 3/2 - 1/2 i)^4 Solution ( -sqrt3/2 -i/2)^4 Polar form = r*e^i*theta r = sqrt[ (-sqrt3/2)^2 + (1/2)^2 )] = 1 theta = tan^-1(-1/2 /-sqrt3/2) = pi +pi/3 = 4pi/3 ( -sqrt3/2 -i/2)^4 = (re^i*theta)^4 = r^4e^i*4theta = 1*e^i*16pi/3 = cos16pi/3 + isin16pi/3 = -0.5 -i*0.866