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stuart clark
07-02-2011, 09:59 AM
If z\in\mathbb{C} and z<\frac{1}{2}, then prove that \left|(1+i).z^3+iz\right|<\frac{3}{4}

mmm4444bot
07-02-2011, 12:48 PM
If z\in\mathbb{C} and 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
07-02-2011, 01:46 PM
actually here |z|<\frac{1}{2}

Subhotosh Khan
07-02-2011, 04:17 PM
If z\in\mathbb{C} and z<\frac{1}{2}, then prove that \left|(1+i).z^3+iz\right|<\frac{3}{4}

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

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.