Here are a few problems on Demoivres Theorem and finding the

Here are a few problems on Demoivre\'s Theorem and finding the nth roots of a complex number. Use DeMoivre\'s Theorem to evaluate (-1 -i squareroot 3)^14. Find the 4 fourth. roots of - 1. Find the 6 sixth roots of -1 + i squareroot 3.

1) z = (-1 - i*sqrt3)^14

r = sqrt(1 +3) = 2 ; theta = 2pi - tan^-1(sqrt3) = pi + pi/3 = 4pi/3

So, z = (re^i*theta) = (2e^i*(4pi/3))^14 = 2^14[cos4pi/3 + i*sin4pi/3]^14

Using De-Movries Theorem : z^n = r^n[ cos(nx) + i*sin(nx) ]

= 2^14[cos(56pi/3) +i*sin(56pi/3) ]

= 2^14[ -1/2 + isqrt3/2]

= 2^13[-1 + i*sqrt3 ]

$Here are a few problems on Demoivre\'s Theorem and finding the nth roots of a complex number. Use DeMoivre\'s Theorem to evaluate (-1 -i squareroot 3)^14. Find$

Here are a few problems on Demoivres Theorem and finding the

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