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 ▸

How do you prove by induction?


Solve the following, giving your answers in terms of ln a: 7 sechx - tanhx =5


Show that the points on an Argand diagram that represent the roots of ((z+1)/z)^6 = 1 lie on a straight line.


Integrate the function f(x) = x ln (x) over the interval [1,e].