Search over 10,000 free study notes

First convert to mod-arg form in order to use de Moivre's theorem. |1 + i| = (1^2 + 1^2)^1/2 = 2^1/2 arg(z) is the angle made by the vector of the complex number and the positive real axis. I world recomm...

S = e^ix - (1/2)e^3ix + (1/4)e^5ix - … is an infinite geometric series, equal to a/(1 - r). a = e^ix and r = (1/2)e^2ix thus S = e^ix/(1+(1/2)e...

The solution like almost every Methods of Differences questions first involves putting the fraction into partial sums.At this point you would get 3 fractions which can be tricky to deal with. Following wh...

We make use of De Moivre's Theorem which states that (cos(θ)+isin(θ))^n=cos(nθ)+isin(nθ).z^n-1/z^n=cos(nθ)+ isin(nθ)-cos(-nθ)- isin(-nθ)=cos(nθ)+ isin(nθ)-cos(nθ)+ isin(nθ) (by trig relat...

We want to simplify this equation to one that we know how to solve. If we let ((z+1)/z) = w, then we need to solve w^6 = 1, which is more familiar. Now we try to find the modulus and argument of w. w = re...