# Thread: complex functions

1. ## complex functions

Hi,

Q1.
a) Find all complex-valued solutions to the equation z^3 - 2z^2 + 4z by hand. Write each one in the form a+bi.

b) Starting with the real-valued root, sketch all the complex-valued cuve roots of -27 in the complex plane. Against each, write its value in the form re^i(feta)

If there is anything unclear in the question, let me know, thanks.

2. Originally Posted by Moon Hoplite
Hi,

Q1.
a) Find all complex-valued solutions to the equation z^3 - 2z^2 + 4z by hand. Write each one in the form a+bi.

Mr F says: z(z^2 - 2z + 4). Factorise the quadratic by first completing the square.

b) Starting with the real-valued root, sketch all the complex-valued cuve roots of -27 in the complex plane. Against each, write its value in the form re^i(feta)
Mr F says: The real root cube root of -27 is -3. All the cube roots lie on a circle of radius 3 and are equally spaced by angle 2 pi/3 ....

If there is anything unclear in the question, let me know, thanks.
..

3. in Q1, how does it mean by giving the answer in the form a+bi?

and in Q2., i still dont get it - is there any key words where i could research the topic based on this question?

4. Originally Posted by Moon Hoplite
in Q1, how does it mean by giving the answer in the form a+bi?
Factor the quadratic and the answer should be clear.