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Confirm my answer plz (1 Viewer)

Thread starter Drsoccerball
Start date Jul 1, 2015

D

Drsoccerball

Well-Known Member

#1

Find the greatest value of |z| if the complex number z satisfies the condition $|z-\frac{4}{z}| =8$
Is the answer: $\frac{8+4\sqrt{5}}{2}$ ?

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InteGrand

Well-Known Member

#2

Drsoccerball said:
Find the greatest value of |z| if the complex number z satisfies the condition $|z-\frac{4}{z}| =8$
Is the answer: $\frac{8+4\sqrt{5}}{2}$ ?

This Q was asked in the HSC 4U Marathon and Ekman got the same answer as you:

Ekman said:
Well your approximations are very accurate:

$|z^2 - 4| = 8|z| \\ |z^2 - 4| \geq |z^2| - 4 \\ \therefore |z^2| - 4 \leq 8|z| \\ |z^2| - 8|z| - 4 \leq 0 \\ |z| \leq \frac{8+\sqrt{80}}{2} \\ |z| \leq 8.47$

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