Complex no.

[stuart clark]

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

[mmm4444bot]

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]

actually here |z|<\frac{1}{2}

[Subhotosh Khan]

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.