Find the 4th roots 6
Express 6 in the exponential form of (6*exp(2πin)), where n is an integertake the fourth root of this, remembering that taking the fourth root is taking to the power of 1/4, and by rules of indices the expression in the exponent must be divided by 4This gives (61/4 *exp(πin/2))Taking n = 0,1,2,3 gives four distinct roots, any larger n gives repeated roots
NP
Answered by Nishil P. • Further Mathematics tutor
4001 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Show that the points on an Argand diagram that represent the roots of ((z+1)/z)^6 = 1 lie on a straight line.
A line has Cartesian equations x−p = (y+2)/q = 3−z and a plane has equation r ∙ [1,−1,−2] = −3. In the case where the angle θ between the line and the plane satisfies sinθ=1/√6 and the line intersects the plane at z = 0. Find p and q.
Let I(n) = integral from 1 to e of (ln(x)^n)/(x^2) dx where n is a natural number. Firstly find I(0). Show that I(n) = -(1/e) + n*I(n-1). Using this formula find I(1).
A particle is moving in a straight line with simple harmonic motion. The period of the motion is (3pi/5)seconds and the amplitude is 0.4metres. Calculate the maximum speed of the particle.