Cube roots of 8?

8 traditionally has 1 cube root. 2. This is only the real root. It has 2 more complex roots!How can we see this?Consider a vector on the argand diagram. If we square it. What happens to it's magnitude and arguement?So as we can see. If 8 is expressed on an argand diagram. The vector at 2 when cubed maps to 8. But can you see the two other points?In general the nth cube root of a complex number has n roots.

VJ

Related Further Mathematics A Level answers

All answers ▸

Use De Moivre's Theorem to show that if z = cos(q)+isin(q), then (z^n)+(z^-n) = 2cos(nq) and (z^n)-(z^-n)=2isin(nq).


When using the method of partial fractions how do you choose what type of numerator to use and how do you know how many partial fractions there are?


Express (X²-16)/(X-1)(X+3) in partial fractions


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.