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}

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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-)

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.

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.

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