latentcorpse said:well you haven't actually written an equation down so there's nothing to solve.
i'm assuming you meant to rewrite it in polar form and then use de moivre
write -12-5i in polar form, that is z=r cis(theta)
where r will be 13 if my mental pythagoras is correct and theta is arctan(y/x)
then use de moivre (-12-5i)^(-3)=z^(-3)=r^(-3) cis(-3 theta)
De Moivre's Theorem is a mathematical theorem that relates to complex numbers. It states that for any complex number z and integer n, (cos θ + i sin θ)n = cos nθ + i sin nθ, where θ is the argument of the complex number.
The formula for De Moivre's Theorem is (cos θ + i sin θ)n = cos nθ + i sin nθ, where θ is the argument of the complex number and n is an integer.
De Moivre's Theorem is used to simplify calculations involving complex numbers by converting them from polar form to rectangular form. It is also used in solving equations involving complex numbers.
Yes, De Moivre's Theorem can be applied to negative exponents. For example, (cos θ + i sin θ)-n = cos -nθ + i sin -nθ = cos nθ - i sin nθ.
To find the nth root of a complex number using De Moivre's Theorem, you would first convert the complex number to polar form, then apply the formula (r(cos θ + i sin θ))1/n = r1/n(cos (θ/n) + i sin (θ/n)). This will give you the nth roots of the complex number in polar form, which can then be converted back to rectangular form if needed.