Find all of the roots of unity, Zn, in the case that (Zn)^6=1

Here we use the complex exponential form of 1 which is e^(i 2n pi). Applying the sixth root and substituting in for integer values of n gives all roots in complex exponential form.These can be converted into a complex number of the form a +ib by using e^ix = cosx +isinx

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The complex number -2sqrt(2) + 2sqrt(6)I can be expressed in the form r*exp(iTheta), where r>0 and -pi < theta <= pi. By using the form r*exp(iTheta) solve the equation z^5 = -2sqrt(2) + 2sqrt(6)i.


z = 4 /(1+ i) Find, in the form a + i b where a, b belong to R, (a) z, (b) z^2. Given that z is a complex root of the quadratic equation x^2 + px + q = 0, where p and q are real integers, (c) find the value of p and the value of q.


Solve (z-i)+(z+i)+(z-1)+(z-1)


Prove by induction that, for all integers n >=1 , ∑(from r=1 to n) r(2r−1)(3r−1)=(n/6)(n+1)(9n^2 -n−2). Assume that 9(k+1)^2 -(k+1)-2=9k^2 +17k+6


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