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
Answered by Vishal J. Further Mathematics tutor

3503 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the modulus-argument form of the complex number z=(5√ 3 - 5i)


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.


Unfortunately this box is to small to contain the question so please see the first paragraph of the answer box for the question.


How do you differentiate x^x?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning