Complex no.

stuart clark

New member
Joined
Mar 3, 2011
Messages
25
If \(\displaystyle z\in\mathbb{C}\) and \(\displaystyle z<\frac{1}{2}\), then prove that \(\displaystyle \left|(1+i).z^3+iz\right|<\frac{3}{4}\)
 


stuart clark said:
If \(\displaystyle z\in\mathbb{C}\) and \(\displaystyle z<\frac{1}{2}\)


The set of Complex numbers is not an ordered set, so how can we state z < 1/2 ?

I mean, the concepts of "greater than" and "less than" do not apply, when talking about numbers with an imaginary part.

Will you please double-check the given information in this exercise? Cheers 8-)

 
stuart clark said:
If \(\displaystyle z\in\mathbb{C}\) and \(\displaystyle z<\frac{1}{2}\), then prove that \(\displaystyle \left|(1+i).z^3+iz\right|<\frac{3}{4}\)

One of the ways to do do this problem would be use:

\(\displaystyle z \ = \ r\cdot e^{(i\theta)}\)

and expand the given expression.

Please share your work with us, indicating exactly where you are stuck, so that we may know where to begin to help you.
 
Top