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i did lots of working and still got no where show that the line x = m(y-1) + 2/m is a tangent to the parabola x^2 = 8(y-1) much help appreciated

here's the questions of the week: (i) a and b are real numbers such that the sum of the squares of the roots of the equation x^2 + (a+ib)x + 3i = 0 is 8. find all possiible pairs of a and b. (ii) 1+ i is a root of the equation x^2 + (a+2i)x + (5+ib) = 0, where a and b are real. find the...

here's the question of the week: if w is a complex cube root of unity, evaluate a+bw+cw^2/b+cw+aw^2 where a, b and c are real numbers. much help appreciated

1. form the equation whose roots are 2+w and 2+w^2, where w is a complex root of unity. 2. if p is one of the complex roots of x^7-1=0, form the equation whose roots are: p+p^2+p^4 and p^6+p^5+p^3. help would be appreciated. thanks

i can do this question by trial and error but i dont know the proper way... z=1+isqrt3. find the smallest positive interger for which z^n is real and evaluate z^n for this value of n. show that there is no integral value of n and for which z^n is imaginary. and... prove that Iz^nI=IzI^n...

what in the world is a feature article? so much for doing extension english.