Complex Number Q (1 Viewer)

[OLDMAN]

ND : you might have made a small computational error. Anyway well done, you're starting to bloom mathematically, on your way to a great medical career.

For interest :
f(a)=|...|^2 where a=cos@
f(a)=4(4a^3-c^2-4a+2) with stationary points given by,
f'(a)=4(12a^2-2a-4)=0 giving a=2/3 or -1/2.
as polynomial f(a) has domain -1<=a<=1 the maximum of f(a) should be one of either -1,-1/2,2/3 or 1. Subbing each of these values into f(a) shows that -1/2 gives the maximum, giving
f(a)=13 or sqrt(13) for the max |z^3-z+2|.

 

[ND]

Originally posted by OLDMAN
ND : you might have made a small computational error. Anyway well done, you're starting to bloom mathematically, on your way to a great medical career.

Praise for an incorrect answer... now that's encouragement!

 

[Richard Lee]

Originally posted by OLDMAN
Following Q has some complex number, some algebra, some trigonometry, some calculus - a good practise question.

Maximize |z^3-z+2| when |z|=1.

|z^3-z+2|=|z(z-1/z)+2|=2|isin@z^2+1|<=2(|iz^2sin@|+1)<=2(sin@+1)<=4

I am not sure if it is right?