Complex Numbers (1 Viewer)

[MrBeefJerky]

Can someone help me with part ii) please
Thank you

 

[QZP]

ii) z^2 - kz + 1 = 0
Therefore z = k +- sqrt (k^2 -4) //2

For z on real axis, discriminant: k^2 - 4 >= 0
i.e. |k| >= 2

For z on unit circle, k^2 - 4 <= 0
i.e. |k| <= 2

 

[bottleofyarn]

From part i) you get two possible conditions (y=0 or x^2 + y^2 = 1) after splitting the real and imaginary parts. Sub these into the real part (relating x, y and k). Then, for the first part it's a simple inequality which you can use by . For the second part, consider the domain of x on the unit circle.

EDIT: QZP's method is also pretty good.